The global dynamics of a discrete SEIR epidemic model with treatment has been considered. A unique positive solution for the proposed model with the positive initial conditions is obtained. The stability analysis of the disease-free equilibrium and endemic equilibrium have been investigated. It has been proved that the DFE is globally asymptotically stable when the basic reproduction number $mathcal{R}_0leq1$. The proposed model has a unique endemic equilibrium that is globally asymptotically stable whenever $tilde{mathcal{R}}_0>1$. The theoretical results are illustrated by a numerical simulation.
{"title":"Global dynamics of a discrete SEIR epidemic model with treatment","authors":"M. DarAssi, Mohammad-Ayman A. Safi","doi":"10.5269/bspm.62203","DOIUrl":"https://doi.org/10.5269/bspm.62203","url":null,"abstract":"The global dynamics of a discrete SEIR epidemic model with treatment has been considered. A unique positive solution for the proposed model with the positive initial conditions is obtained. The stability analysis of the disease-free equilibrium and endemic equilibrium have been investigated. It has been proved that the DFE is globally asymptotically stable when the basic reproduction number $mathcal{R}_0leq1$. The proposed model has a unique endemic equilibrium that is globally asymptotically stable whenever $tilde{mathcal{R}}_0>1$. The theoretical results are illustrated by a numerical simulation.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46288557","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}
This paper is devoted to study some regularity of almost automorphic and asymptotic almost automorphic generalized solution of the differential equation d dtu(t) = Au(t) + f(t), in the framework of the Colombeau algebras. Under certain assumptions about the second member we showed that the generalized solution is an asmptotically almost automorphic in the sense of genaralized functions.
{"title":"On the existence of almost automorphic generalized solutions to some generalized differential equations","authors":"Mohamed Elomari, M. Chaib, S. Melliani","doi":"10.5269/bspm.63116","DOIUrl":"https://doi.org/10.5269/bspm.63116","url":null,"abstract":"This paper is devoted to study some regularity of almost automorphic and asymptotic almost automorphic generalized solution of the differential equation d dtu(t) = Au(t) + f(t), in the framework of the Colombeau algebras. Under certain assumptions about the second member we showed that the generalized solution is an asmptotically almost automorphic in the sense of genaralized functions.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41333036","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}
This paper deals with the existence of multiple solutions for the following critical fractional $p$-Laplacian problem begin{equation*} left{ begin{array}{l} mathbf{(-}Delta mathbf{)}_{p}^{s}u(x)=lambda leftvert urightvert ^{p-2}u+f(x,u)+mu g(x,u) text{in }Omega ,u>0, u=0text{ on} mathbb{R}^{n}setminus Omega ,% end{array}% right. end{equation*}% where $p>1$, $sin (0,1)$, $Omega subset mathbb{R}^{n}(n>ps),$ be a bounded smooth domain, $lambda $, $mu $ are positive parameters and the functions $f,g:overline{% Omega }times lbrack 0,infty )longrightarrow [0,infty),$ are continuous and differentiable with respect to the second variable. Our main tools are based on variational methods combined with a classical concentration compacteness method.
{"title":"The multiplicity of solutions for the critical problem involving the fracional p-Laplacian operator","authors":"Djamel Abid, K. Akrout, A. Ghanmi","doi":"10.5269/bspm.62706","DOIUrl":"https://doi.org/10.5269/bspm.62706","url":null,"abstract":"This paper deals with the existence of multiple solutions \u0000for the following critical fractional $p$-Laplacian problem \u0000begin{equation*} \u0000left{ \u0000begin{array}{l} \u0000mathbf{(-}Delta mathbf{)}_{p}^{s}u(x)=lambda leftvert urightvert \u0000^{p-2}u+f(x,u)+mu g(x,u) text{in }Omega ,u>0, \u0000 \u0000u=0text{ on} mathbb{R}^{n}setminus Omega ,% \u0000end{array}% \u0000right. \u0000end{equation*}% \u0000where $p>1$, $sin (0,1)$, $Omega subset mathbb{R}^{n}(n>ps),$ be a bounded smooth domain, $lambda $, $mu $ are positive parameters and the functions $f,g:overline{% \u0000Omega }times lbrack 0,infty )longrightarrow [0,infty),$ are continuous and differentiable with respect to the second variable. Our main tools are based on variational methods combined with a classical concentration \u0000compacteness method.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44509207","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}
This paper considers the existence of entropy solutions for some generalized elliptic p(u)-Laplacian problem with Fourier boundary conditions, when the variable exponent p is a real continuous function and we have dependency on the solution u. We get the results by assuming the right-hand sidefunction f to be an integrable function, and by using the regularization approach combined with the theoryof Sobolev spaces with variable exponents.
{"title":"Nonlinear elliptic problems involving the generalized p(u)-Laplacian operator with Fourier boundary condition","authors":"C. Allalou, Said Ait Temghart, K. Hilal","doi":"10.5269/bspm.62948","DOIUrl":"https://doi.org/10.5269/bspm.62948","url":null,"abstract":"This paper considers the existence of entropy solutions for some generalized elliptic p(u)-Laplacian problem with Fourier boundary conditions, when the variable exponent p is a real continuous function and we have dependency on the solution u. We get the results by assuming the right-hand sidefunction f to be an integrable function, and by using the regularization approach combined with the theoryof Sobolev spaces with variable exponents.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48121057","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 aim of this paper deals with the existence results for a class of fractional langevin inclusion with multi-point boundary conditions. To prove the main results, we use the fixed theoreme for condensing multivalued maps, which is applicable to completely continuous operators. Our results extend and generalize several corespending results from the existing literature.
{"title":"On a class of fractional Langevin inclusion with multi-point boundary conditions","authors":"Hamid Lmou, K. Hilal, A. Kajouni","doi":"10.5269/bspm.62725","DOIUrl":"https://doi.org/10.5269/bspm.62725","url":null,"abstract":"The aim of this paper deals with the existence results for a class of fractional langevin inclusion with multi-point boundary conditions. To prove the main results, we use the fixed theoreme for condensing multivalued maps, which is applicable to completely continuous operators. Our results extend and generalize several corespending results from the existing literature.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49348208","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}
A G−graded R−module is called flexible if Mg = RgMe for every g ∈ G. In this paper, we study the relationship between a flexible module and the graded ring R through different aspects. On one hand, we distinguish the flexible modules from other graded modules by characterizing the influence of the e-component of a flexiblemodule on the graded module itself. On the other hand, we extend the class covered by flexible graded modules to include free and projective modules in a comparatively simple manner.
{"title":"Flexible modules and graded rings","authors":"Fida Moh'd, Mamoon Ahmed, Mashoor Refai","doi":"10.5269/bspm.62550","DOIUrl":"https://doi.org/10.5269/bspm.62550","url":null,"abstract":"A G−graded R−module is called flexible if Mg = RgMe for every g ∈ G. In this paper, we study the relationship between a flexible module and the graded ring R through different aspects. On one hand, we distinguish the flexible modules from other graded modules by characterizing the influence of the e-component of a flexiblemodule on the graded module itself. On the other hand, we extend the class covered by flexible graded modules to include free and projective modules in a comparatively simple manner.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49566911","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}
In the present paper, in view of the topological degree methods and the theory of the variable exponent Sobolev spaces, we discuss a Dirichlet boundary value problem for elliptic equations involving the $(p(x),q(x))$-Laplacian operator with a reaction term depending on the gradient and on two real parameters. Under certain assumptions, we establish the existence of at least one weak solution to this problem. Our results extends some recent work in the literature.
{"title":"Weak solutions for double phase problem driven by the (p(x),q(x))-Laplacian operator under Dirichlet boundary conditions","authors":"Mohamed El Ouaarabi, C. Allalou, S. Melliani","doi":"10.5269/bspm.62182","DOIUrl":"https://doi.org/10.5269/bspm.62182","url":null,"abstract":"In the present paper, in view of the topological degree methods and the theory of the variable exponent Sobolev spaces, we discuss a Dirichlet boundary value problem for elliptic equations involving the $(p(x),q(x))$-Laplacian operator with a reaction term depending on the gradient and on two real parameters. Under certain assumptions, we establish the existence of at least one weak solution to this problem. Our results extends some recent work in the literature.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48976659","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}
This study develops some results involving generalized homoderivation in semiprime rings and investigates the commutativity of semiprime rings admitting generalized homoderivations of ring R satisfying certain identities and some related results have also been discussed.
{"title":"Semiprime rings with generalized homoderivations","authors":"A. Boua, Emine Koc Sogutcu","doi":"10.5269/bspm.62479","DOIUrl":"https://doi.org/10.5269/bspm.62479","url":null,"abstract":"This study develops some results involving generalized homoderivation in semiprime rings and investigates the commutativity of semiprime rings admitting generalized homoderivations of ring R satisfying certain identities and some related results have also been discussed.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42110050","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}
Let R be an associative ring, P a prime ideal of R: In this paper, we study the structure of the ring R=P and describe the possible forms of the generalized derivations satisfying certain algebraic identities on R: As a consequence of our theorems, we first investigate strong commutativity preserving generalized derivations of prime rings, and then examine the generalized derivations acting as (anti)homomorphisms in prime rings. Some commutativity theorems also given in semi-prime rings.
{"title":"Some identities in quotient rings","authors":"Mouhamadi El Hamdaoui, A. Boua, G. Sandhu","doi":"10.5269/bspm.62481","DOIUrl":"https://doi.org/10.5269/bspm.62481","url":null,"abstract":"Let R be an associative ring, P a prime ideal of R: In this paper, we study the structure of the ring R=P and describe the possible forms of the generalized derivations satisfying certain algebraic identities on R: As a consequence of our theorems, we first investigate strong commutativity preserving generalized derivations of prime rings, and then examine the generalized derivations acting as (anti)homomorphisms in prime rings. Some commutativity theorems also given in semi-prime rings.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46661170","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}
Let R be a ring and P be a prime ideal of R: In this work, we study the structure of the quotient ring R=P in a new and more general way by discussing various algebraic identities on appropriate subsets of R involving multiplicative (generalized)-(α; β)-derivations, multiplicative generalized (α; β)-derivations, multiplicative generalized derivations and generalized derivations. In addition, we give examples exhibiting the cruciality of the hypothesis of our results.
{"title":"Results on various derivations and Posner’s theorem in prime ideals of rings","authors":"A. Boua, G. Sandhu","doi":"10.5269/bspm.62478","DOIUrl":"https://doi.org/10.5269/bspm.62478","url":null,"abstract":"Let R be a ring and P be a prime ideal of R: In this work, we study the structure of the quotient ring R=P in a new and more general way by discussing various algebraic identities on appropriate subsets of R involving multiplicative (generalized)-(α; β)-derivations, multiplicative generalized (α; β)-derivations, multiplicative generalized derivations and generalized derivations. In addition, we give examples exhibiting the cruciality of the hypothesis of our results.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44174708","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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