Pub Date : 2021-11-16DOI: 10.21136/mb.2021.0122-20
A. Khaldi, Amar Ouaoua, M. Maouni
We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms ut −M ( ∫
我们考虑一类具有变指数和源项ut−M（ξ
{"title":"Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents","authors":"A. Khaldi, Amar Ouaoua, M. Maouni","doi":"10.21136/mb.2021.0122-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0122-20","url":null,"abstract":"We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms ut −M ( ∫","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46343051","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 : 2021-11-15DOI: 10.21136/mb.2021.0172-20
Agus L. Soenjaya
Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in (u, n) ∈ L × L under some conditions on the nonlinearity (the coupling term), by using the L conservation law for u and controlling the growth of n via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007) for some exponents to other dimensions and in lower regularity spaces.
{"title":"Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling","authors":"Agus L. Soenjaya","doi":"10.21136/mb.2021.0172-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0172-20","url":null,"abstract":"Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in (u, n) ∈ L × L under some conditions on the nonlinearity (the coupling term), by using the L conservation law for u and controlling the growth of n via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007) for some exponents to other dimensions and in lower regularity spaces.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42106866","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 : 2021-10-18DOI: 10.21136/mb.2021.0058-21
P. Karmakar
The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ-projectively flat, M -projectively flat, ξ-M -projectively flat, pseudo projectively flat and ξ-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, M -projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.
{"title":"Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold","authors":"P. Karmakar","doi":"10.21136/mb.2021.0058-21","DOIUrl":"https://doi.org/10.21136/mb.2021.0058-21","url":null,"abstract":"The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ-projectively flat, M -projectively flat, ξ-M -projectively flat, pseudo projectively flat and ξ-pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on Ricci flat, concircularly flat, M -projectively flat and pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting the aforesaid connection are studied. At last, some conclusions are made after observing all the results and an example of an anti-invariant submanifold of a trans-Sasakian manifold is given in which all the results can be verified easily.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47982740","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 : 2021-09-09DOI: 10.21136/mb.2021.0079-20
Mimia Benhadri, T. Caraballo
This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.
{"title":"New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations","authors":"Mimia Benhadri, T. Caraballo","doi":"10.21136/mb.2021.0079-20","DOIUrl":"https://doi.org/10.21136/mb.2021.0079-20","url":null,"abstract":"This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46807442","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 : 2021-08-22DOI: 10.21136/mb.2022.0127-21
D. C. Mayer
. For any number field K with non-elementary 3-class group Cl 3 ( K ) ≃ C 3 e × C 3 , e > 2, the punctured capitulation type κ ( K ) of K in its unramified cyclic cubic extensions L i , 1 6 i 6 4, is an orbit under the action of S 3 × S 3 . By means of Artin’s reciprocity law, the arithmetical invariant κ ( K ) is translated to the punctured transfer kernel type κ ( G 2 ) of the automorphism group G 2 = Gal(F 23 ( K ) /K ) of the second Hilbert 3-class field of K . A classification of finite 3-groups G with low order and bicyclic commutator quotient G/G ′ ≃ C 3 e × C 3 , 2 6 e 6 6, according to the algebraic invariant κ ( G ), admits conclu-sions concerning the length of the Hilbert 3-class field tower F ∞ 3 ( K ) of imaginary quadratic number fields K .
.对于具有非初等3类群Cl3（K）-C3e×C3，e>2的任何数域K，K在其未分支的循环三次扩张L i，16 i 6 4中的穿孔投降型κ（K）是在S3×S3作用下的轨道。利用Artin互易律，将算术不变量κ（K）转化为K的第二个Hilbert 3类域的自同构群G2＝Gal（F23（K）/K）的删截转移核型κ（G2）。根据代数不变量κ（G），给出了具有低阶双环交换商G/G′-C3e×C3，2 6e 6的有限3-群G的一个分类，得到了关于虚二次域K的Hilbert 3-类域塔F∞3（K）的长度的结论。
{"title":"Bicyclic commutator quotients with one non-elementary component","authors":"D. C. Mayer","doi":"10.21136/mb.2022.0127-21","DOIUrl":"https://doi.org/10.21136/mb.2022.0127-21","url":null,"abstract":". For any number field K with non-elementary 3-class group Cl 3 ( K ) ≃ C 3 e × C 3 , e > 2, the punctured capitulation type κ ( K ) of K in its unramified cyclic cubic extensions L i , 1 6 i 6 4, is an orbit under the action of S 3 × S 3 . By means of Artin’s reciprocity law, the arithmetical invariant κ ( K ) is translated to the punctured transfer kernel type κ ( G 2 ) of the automorphism group G 2 = Gal(F 23 ( K ) /K ) of the second Hilbert 3-class field of K . A classification of finite 3-groups G with low order and bicyclic commutator quotient G/G ′ ≃ C 3 e × C 3 , 2 6 e 6 6, according to the algebraic invariant κ ( G ), admits conclu-sions concerning the length of the Hilbert 3-class field tower F ∞ 3 ( K ) of imaginary quadratic number fields K .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46661907","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 : 2021-07-13DOI: 10.21136/MB.2021.0081-19
J. Graef, D. Beldjerd, M. Remili
The authors establish some new sufficient conditions under which all solutions of a certain class of nonlinear neutral delay differential equations of the third order are stable, bounded, and square integrable. Illustrative examples are given to demonstrate the main results.
{"title":"On stability, boundedness, and square integrability of solutions of certain third order neutral differential equations","authors":"J. Graef, D. Beldjerd, M. Remili","doi":"10.21136/MB.2021.0081-19","DOIUrl":"https://doi.org/10.21136/MB.2021.0081-19","url":null,"abstract":"The authors establish some new sufficient conditions under which all solutions of a certain class of nonlinear neutral delay differential equations of the third order are stable, bounded, and square integrable. Illustrative examples are given to demonstrate the main results.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45129892","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 : 2021-07-12DOI: 10.21136/MB.2021.0109-20
G. Chatzarakis, Ponnuraj Dinakar, S. Selvarangam, E. Thandapani
{"title":"Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms","authors":"G. Chatzarakis, Ponnuraj Dinakar, S. Selvarangam, E. Thandapani","doi":"10.21136/MB.2021.0109-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0109-20","url":null,"abstract":"","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031461","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 : 2021-07-08DOI: 10.21136/MB.2021.0073-20
B. U. Afsan, Javier Gutiérrez García
In 2005, İ. Tok fuzzified the notion of the topological entropy R.A.Adler et al. (1965) using the notion of fuzzy compactness of C. L.Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R.A.Adler et al. (1965) of continuous mapping ψ : (X, τ)→ (X, τ), where (X, τ) is compact, is equal to the weakly fuzzy topological entropy of ψ : (X,ω(τ))→ (X,ω(τ)). We have also established an example that shows that the fuzzy topological entropy of İ. Tok (2005) cannot give such a bridge result to the topological entropy of Adler et al. (1965). Moreover, our definition of the weakly fuzzy topological entropy can be applied to find the topological entropy (namely weakly fuzzy topological entropy hw(ψ)) of the mapping ψ : X → X (where X is either compact or weakly fuzzy compact), whereas the topological entropy ha(ψ) of Adler does not exist for the mapping ψ : X → X (where X is non-compact weakly fuzzy compact). Finally, a product theorem for the weakly fuzzy topological entropy has been established.
{"title":"Weakly fuzzy topological entropy","authors":"B. U. Afsan, Javier Gutiérrez García","doi":"10.21136/MB.2021.0073-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0073-20","url":null,"abstract":"In 2005, İ. Tok fuzzified the notion of the topological entropy R.A.Adler et al. (1965) using the notion of fuzzy compactness of C. L.Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R.A.Adler et al. (1965) of continuous mapping ψ : (X, τ)→ (X, τ), where (X, τ) is compact, is equal to the weakly fuzzy topological entropy of ψ : (X,ω(τ))→ (X,ω(τ)). We have also established an example that shows that the fuzzy topological entropy of İ. Tok (2005) cannot give such a bridge result to the topological entropy of Adler et al. (1965). Moreover, our definition of the weakly fuzzy topological entropy can be applied to find the topological entropy (namely weakly fuzzy topological entropy hw(ψ)) of the mapping ψ : X → X (where X is either compact or weakly fuzzy compact), whereas the topological entropy ha(ψ) of Adler does not exist for the mapping ψ : X → X (where X is non-compact weakly fuzzy compact). Finally, a product theorem for the weakly fuzzy topological entropy has been established.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46951013","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 : 2021-07-08DOI: 10.21136/MB.2021.0094-20
B. Nam, N. Nhan, L. Ngoc, N. Long
We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.
{"title":"On a system of nonlinear wave equations with the Kirchhoff-Carrier\u0000 \u0000and Balakrishnan-Taylor terms","authors":"B. Nam, N. Nhan, L. Ngoc, N. Long","doi":"10.21136/MB.2021.0094-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0094-20","url":null,"abstract":"We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44010042","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 : 2021-03-08DOI: 10.21136/MB.2021.0104-20
R. Sharma, Gaurav Mittal
. We give the characterization of the unit group of F q SL (2 , Z 5 ), where F q is a finite field with q = p k elements for prime p > 5 , and SL (2 , Z 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group Z 5 .
{"title":"On the unit group of a semisimple group algebra $mathbb{F}_qSL(2, mathbb{Z}_5)$","authors":"R. Sharma, Gaurav Mittal","doi":"10.21136/MB.2021.0104-20","DOIUrl":"https://doi.org/10.21136/MB.2021.0104-20","url":null,"abstract":". We give the characterization of the unit group of F q SL (2 , Z 5 ), where F q is a finite field with q = p k elements for prime p > 5 , and SL (2 , Z 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group Z 5 .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46787899","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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