Pub Date : 2022-08-29DOI: 10.21136/mb.2022.0010-22
J. Farley
. Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that P is connected and P P ∼ = Q Q imply that Q is connected”, where P and Q are finite nonempty posets. We show that, indeed, under these hypotheses Q is connected and P ∼ = Q .
． Duffus在1978年的博士论文中写道，“P是连通的，P P ~ = Q Q暗示Q是连通的，这是不明显的”，其中P和Q是有限的非空偏集。我们证明，在这些假设下，Q是连通的，P ~ = Q。
{"title":"Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected?\u0000 \u0000An issue Duffus raised in 1978","authors":"J. Farley","doi":"10.21136/mb.2022.0010-22","DOIUrl":"https://doi.org/10.21136/mb.2022.0010-22","url":null,"abstract":". Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that P is connected and P P ∼ = Q Q imply that Q is connected”, where P and Q are finite nonempty posets. We show that, indeed, under these hypotheses Q is connected and P ∼ = Q .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41537603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The studies considered here are concerend with a linear thermoelastic Bresse system with delay term in the feedback. The heat conduction is also given by Cattaneo’s law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method. Furthermore, based on the energy method, we establish an exponential stability result depending of a condition on the constants of the system that was first considered by A. Keddi, T. Apalara, S. A. Messaoudi in 2018.
． 本文研究的是反馈中有时滞项的线性热弹性Bresse系统。热传导也由卡塔尼奥定律给出。在时滞权值与阻尼权值之间适当的假设下，用半群方法证明了问题的适定性。此外，基于能量法，我们根据a . Keddi, T. Apalara, S. a . Messaoudi于2018年首次考虑的系统常数条件建立了指数稳定性结果。
{"title":"Stability result for a thermoelastic Bresse system with delay term in the internal feedback","authors":"Bouzettouta Lamine, Baibeche Sabah, Abdelli Manel, Guesmia Amar","doi":"10.21136/mb.2022.0154-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0154-21","url":null,"abstract":". The studies considered here are concerend with a linear thermoelastic Bresse system with delay term in the feedback. The heat conduction is also given by Cattaneo’s law. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method. Furthermore, based on the energy method, we establish an exponential stability result depending of a condition on the constants of the system that was first considered by A. Keddi, T. Apalara, S. A. Messaoudi in 2018.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45786264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-04DOI: 10.21136/mb.2022.0088-21
Y. Echarroudi
ly, a functional response can be defined as the relationship between an individual’s rate of consumption (here we talk about a consumption of predator) and food’s density (i.e., prey’s density). This amounts to saying that a functional response reflects the capture ability of the predator to prey or in other words, the functional response is introduced to describe the change in the rate of consumption of prey by predator when the density of prey varies. In the plotting point of view, each type of functional response I, II or III has a special characteristic. In fact, type I, or the linear case of the predator response, is the situation when the plot of the number of prey consumed (per unit of time) as a function of prey density shows a linear relationship between the number of prey consumed and the prey density. The Holling type II, called also concave upward response, is the case when the gradient of the curve decreases monotonically with increasing prey density, probably saturating at a constant value of prey consumption. For information, the Lotka-Volterra model involving this functional response is known as the Rosenzweig-MacArthur model. The type III response is known between the specialists of population dynamics as the sigmoid response having a concave downward part at low food density. Actually, for the Holling III, a sigmoidal behavior occurs when the gradient of the curve first increases and then decreases with increasing prey density. This behavior is due to the “learning behavior” in the predator population. Now, we address some “ecological” interpretations of the three first Holling types functional responses. The type I response is the result of simple assumption that the probability of a given predator (usually the passive one) encountering prey in a fixed time interval [0, Tt] within a fixed spatial region depends linearly on the prey density. This can be expressed under the form Y = aTsX, where Y is the amount of prey consumed by one predator, X is the prey density, Ts is the time available for searching and a is a constant of proportionality, termed as the discovery rate (which is in our case represented by the parameter b). In the absence of need to spend time handling the prey, all the time can be used for searching, i.e., Ts = Tt, and we have the type I response: assuming that the predators (having the density P ) act independently, in time Tt the total amount of prey will be reduced by quantity aTtXP . In addition, if each predator requires a handling time h for each individual prey that is consumed, the time available for searching Ts is reduced: Ts = Tt−hY . Taking into account the expression of Y in response type I, this leads to Y = aTtX − ahXY and this implies Y = aTtX/(1 + ahX) and this is exactly the type II response. Therefore, in the interval [0, Tt] the total amount of prey is reduced by the quantity aTtXP/(1 + ahX). Let us point out that the term “ah” is dimensionless and can be interpreted as the ability of a gen
{"title":"Null controllability of a coupled model in population dynamics","authors":"Y. Echarroudi","doi":"10.21136/mb.2022.0088-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0088-21","url":null,"abstract":"ly, a functional response can be defined as the relationship between an individual’s rate of consumption (here we talk about a consumption of predator) and food’s density (i.e., prey’s density). This amounts to saying that a functional response reflects the capture ability of the predator to prey or in other words, the functional response is introduced to describe the change in the rate of consumption of prey by predator when the density of prey varies. In the plotting point of view, each type of functional response I, II or III has a special characteristic. In fact, type I, or the linear case of the predator response, is the situation when the plot of the number of prey consumed (per unit of time) as a function of prey density shows a linear relationship between the number of prey consumed and the prey density. The Holling type II, called also concave upward response, is the case when the gradient of the curve decreases monotonically with increasing prey density, probably saturating at a constant value of prey consumption. For information, the Lotka-Volterra model involving this functional response is known as the Rosenzweig-MacArthur model. The type III response is known between the specialists of population dynamics as the sigmoid response having a concave downward part at low food density. Actually, for the Holling III, a sigmoidal behavior occurs when the gradient of the curve first increases and then decreases with increasing prey density. This behavior is due to the “learning behavior” in the predator population. Now, we address some “ecological” interpretations of the three first Holling types functional responses. The type I response is the result of simple assumption that the probability of a given predator (usually the passive one) encountering prey in a fixed time interval [0, Tt] within a fixed spatial region depends linearly on the prey density. This can be expressed under the form Y = aTsX, where Y is the amount of prey consumed by one predator, X is the prey density, Ts is the time available for searching and a is a constant of proportionality, termed as the discovery rate (which is in our case represented by the parameter b). In the absence of need to spend time handling the prey, all the time can be used for searching, i.e., Ts = Tt, and we have the type I response: assuming that the predators (having the density P ) act independently, in time Tt the total amount of prey will be reduced by quantity aTtXP . In addition, if each predator requires a handling time h for each individual prey that is consumed, the time available for searching Ts is reduced: Ts = Tt−hY . Taking into account the expression of Y in response type I, this leads to Y = aTtX − ahXY and this implies Y = aTtX/(1 + ahX) and this is exactly the type II response. Therefore, in the interval [0, Tt] the total amount of prey is reduced by the quantity aTtXP/(1 + ahX). Let us point out that the term “ah” is dimensionless and can be interpreted as the ability of a gen","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47907778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-03DOI: 10.21136/mb.2022.0096-21
N. Gürses, G. Y. Şentürk, S. Yüce
. We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values α , β and p . Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given.
{"title":"Investigating generalized quaternions with dual-generalized complex numbers","authors":"N. Gürses, G. Y. Şentürk, S. Yüce","doi":"10.21136/mb.2022.0096-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0096-21","url":null,"abstract":". We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values α , β and p . Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45494174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-03DOI: 10.21136/mb.2022.0166-21
D. O. Adams, M. Omeike, I. Osinuga, B. S. Badmus
. We consider certain class of second order nonlinear nonautonomous delay differential equations of the form where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovskiˇı functional to establish our results. This work extends and improve on some results in the literature.
{"title":"Boundedness criteria for a class of second order nonlinear differential equations with delay","authors":"D. O. Adams, M. Omeike, I. Osinuga, B. S. Badmus","doi":"10.21136/mb.2022.0166-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0166-21","url":null,"abstract":". We consider certain class of second order nonlinear nonautonomous delay differential equations of the form where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovskiˇı functional to establish our results. This work extends and improve on some results in the literature.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45989348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-02DOI: 10.21136/mb.2023.0108-22
I. Chajda, Miroslav Kolavr'ik, H. Langer
In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, respectively, and we prove basic properties of them. Finally, we prove so-called Separation Theorems for c-ideals. The text is illustrated by several examples.
{"title":"c-ideals in complemented posets","authors":"I. Chajda, Miroslav Kolavr'ik, H. Langer","doi":"10.21136/mb.2023.0108-22","DOIUrl":"https://doi.org/10.21136/mb.2023.0108-22","url":null,"abstract":"In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, respectively, and we prove basic properties of them. Finally, we prove so-called Separation Theorems for c-ideals. The text is illustrated by several examples.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49454673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-11DOI: 10.21136/mb.2022.0110-21
R. Shroff
. Absolute direct summand in lattices is defined and some of its properties in modular lattices are studied. It is shown that in a certain class of modular lattices, the direct sum of two elements has absolute direct summand if and only if the elements are relatively injective. As a generalization of absolute direct summand (ADS for short), the concept of Goldie absolute direct summand in lattices is introduced and studied. It is shown that Goldie ADS property is inherited by direct summands. A necessary and sufficient condition is given for an element of modular lattice to have Goldie ADS.
{"title":"On Goldie absolute direct summands in modular lattices","authors":"R. Shroff","doi":"10.21136/mb.2022.0110-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0110-21","url":null,"abstract":". Absolute direct summand in lattices is defined and some of its properties in modular lattices are studied. It is shown that in a certain class of modular lattices, the direct sum of two elements has absolute direct summand if and only if the elements are relatively injective. As a generalization of absolute direct summand (ADS for short), the concept of Goldie absolute direct summand in lattices is introduced and studied. It is shown that Goldie ADS property is inherited by direct summands. A necessary and sufficient condition is given for an element of modular lattice to have Goldie ADS.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42393366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-10DOI: 10.21136/mb.2023.0162-22
U. M. Hanung
Various kinds of Stieltjes integrals using gauge integration have become highly popular in the field of differential equations and other applications. In the theories of integration and of ordinary differential equations, convergence theorems provide one of the most widely used tools. The Harnack extension principle, which discusses a sufficient condition for Kurzweil-Henstock integrable functions on particular subsets of $(a,b)$ to be integrable on $[a,b]$, is a key step to supply convergence theorems. The Kurzweil-Stieltjes integral reduces to the Kurzweil-Henstock integral whenever the integrator is an identity function. In general, if the integrator $F$ is discontinuous on $[c,d]subset[a,b]$, then the values of the Kurzweil-Stieltjes integrals $$int_c^d[dF]g, int_{[c,d]}[dF]g, int_{[c,d)}[dF]g, int_{(c,d]}[dF]g, {rm and} int_{(c,d)}[dF]g$$ need not coincide. Hence, the Harnack extension principle in the Kurzweil-Henstock integral cannot be valid any longer for the Kurzweil-type Stieltjes integrals with discontinuous integrators. The new concepts of equi-integrability and equiregulatedness are pivotal to the notion of the Harnack extension principle for the Kurzweil-Stieltjes integration. Moreover, the existence of the integral $int_a^b[dF]g$ does not (even in the case of the identity integrator) always imply the existence of the integral $int_{T}[dF]g$ for every subset $T$ of $[a,b]$. This follows from the well-known fact that, if e.g., $Tsubset[a,b]$ is not measurable, then the existence of the Lebesgue integral $int_a^b g [dt]$ does not imply that the integral $int_T g [dt]$ exists. Therefore, besides constructing the Harnack extension principle for the abstract Kurzweil-Stieltjes integral, the aim of this paper is also to demonstrate its role in guaranteeing the existence of the integrals $int_{T}[dF]g$ for arbitrary subsets $T$ of an elementary set $E$.
利用规范积分的各种Stieltjes积分在微分方程和其他应用领域得到了广泛的应用。在积分理论和常微分方程中，收敛定理是应用最广泛的工具之一。利用Harnack扩展原理，讨论了$(a,b)$的特定子集上的Kurzweil-Henstock可积函数在$[a,b]$上可积的充分条件，是给出收敛定理的关键步骤。当积分器是恒等函数时，Kurzweil-Stieltjes积分化为Kurzweil-Henstock积分。一般来说，如果积分器$F$在$[c,d]subset[a,b]$上是不连续的，那么Kurzweil-Stieltjes积分$$int_c^d[dF]g, int_{[c,d]}[dF]g, int_{[c,d)}[dF]g, int_{(c,d]}[dF]g, {rm and} int_{(c,d)}[dF]g$$的值不必重合。因此，对于具有不连续积分器的kurzweil型Stieltjes积分，Kurzweil-Henstock积分中的Harnack扩展原理不再有效。对于Kurzweil-Stieltjes积分的Harnack可拓原理的概念来说，等可积性和等正则性的新概念至关重要。此外，积分$int_a^b[dF]g$的存在性并不总是意味着对于$[a,b]$的每个子集$T$的积分$int_{T}[dF]g$的存在性(即使在单位积分器的情况下)。这源于一个众所周知的事实，即如果例如$Tsubset[a,b]$不可测量，那么勒贝格积分$int_a^b g [dt]$的存在并不意味着积分$int_T g [dt]$的存在。因此，本文除了构造抽象Kurzweil-Stieltjes积分的Harnack可拓原理外，还证明了它在保证初等集合$E$的任意子集$T$的积分$int_{T}[dF]g$存在性方面的作用。
{"title":"Role of the Harnack extension principle in the Kurzweil-Stieltjes integral","authors":"U. M. Hanung","doi":"10.21136/mb.2023.0162-22","DOIUrl":"https://doi.org/10.21136/mb.2023.0162-22","url":null,"abstract":"Various kinds of Stieltjes integrals using gauge integration have become highly popular in the field of differential equations and other applications. In the theories of integration and of ordinary differential equations, convergence theorems provide one of the most widely used tools. The Harnack extension principle, which discusses a sufficient condition for Kurzweil-Henstock integrable functions on particular subsets of $(a,b)$ to be integrable on $[a,b]$, is a key step to supply convergence theorems. The Kurzweil-Stieltjes integral reduces to the Kurzweil-Henstock integral whenever the integrator is an identity function. In general, if the integrator $F$ is discontinuous on $[c,d]subset[a,b]$, then the values of the Kurzweil-Stieltjes integrals $$int_c^d[dF]g, int_{[c,d]}[dF]g, int_{[c,d)}[dF]g, int_{(c,d]}[dF]g, {rm and} int_{(c,d)}[dF]g$$ need not coincide. Hence, the Harnack extension principle in the Kurzweil-Henstock integral cannot be valid any longer for the Kurzweil-type Stieltjes integrals with discontinuous integrators. The new concepts of equi-integrability and equiregulatedness are pivotal to the notion of the Harnack extension principle for the Kurzweil-Stieltjes integration. Moreover, the existence of the integral $int_a^b[dF]g$ does not (even in the case of the identity integrator) always imply the existence of the integral $int_{T}[dF]g$ for every subset $T$ of $[a,b]$. This follows from the well-known fact that, if e.g., $Tsubset[a,b]$ is not measurable, then the existence of the Lebesgue integral $int_a^b g [dt]$ does not imply that the integral $int_T g [dt]$ exists. Therefore, besides constructing the Harnack extension principle for the abstract Kurzweil-Stieltjes integral, the aim of this paper is also to demonstrate its role in guaranteeing the existence of the integrals $int_{T}[dF]g$ for arbitrary subsets $T$ of an elementary set $E$.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48524672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-27DOI: 10.21136/mb.2022.0069-21
Sungchol Kim, Dukman Ri
. This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type where Ω is a bounded domain of R n , n > 2. In particular, we do not require strict monotonicity of the principal part a ( x, z, · ), while the approach is based on the variational method and results of the variable exponent function spaces.
{"title":"Existence of weak solutions for elliptic Dirichlet problems with variable exponent","authors":"Sungchol Kim, Dukman Ri","doi":"10.21136/mb.2022.0069-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0069-21","url":null,"abstract":". This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type where Ω is a bounded domain of R n , n > 2. In particular, we do not require strict monotonicity of the principal part a ( x, z, · ), while the approach is based on the variational method and results of the variable exponent function spaces.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46707297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-23DOI: 10.21136/mb.2022.0061-21
Y. Akdim, M. Belayachi, H. Hjiaj
. This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by where Ω is a bounded open set of R N ( N > 2) with 1 < p < N and f ∈ L 1 (Ω) , under some growth conditions on the function b ( · ) and d ( · ) , where c ( · ) is assumed to be in L N/ ( p − 1) (Ω) . We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded.
． 本文研究了一类非线性退化椭圆型方程，其原型为:Ω是R N (N > 2)的有界开集，1 < p < N, f∈l1 (Ω)，在函数b(·)和d(·)的某些生长条件下，假设c(·)在L N/ (p−1)(Ω)中。我们证明了该非强制椭圆方程重整解的存在性，并得到了一些正则性结果。
{"title":"Existence of renormalized solutions for some degenerate and non-coercive elliptic equations","authors":"Y. Akdim, M. Belayachi, H. Hjiaj","doi":"10.21136/mb.2022.0061-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0061-21","url":null,"abstract":". This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by where Ω is a bounded open set of R N ( N > 2) with 1 < p < N and f ∈ L 1 (Ω) , under some growth conditions on the function b ( · ) and d ( · ) , where c ( · ) is assumed to be in L N/ ( p − 1) (Ω) . We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45779416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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