. This paper aims at establishing the multiplicity results of nontrivial weak solutions for impulsive elastic beam equations of the Kirchhoff-type. The approach follows variational methods and the critical point theory.
{"title":"Nontrivial solutions for impulsive elastic beam equations of Kirchhoff-type","authors":"S. Heidarkhani, G. Caristi, Amjad Salari","doi":"10.23952/jnfa.2020.4","DOIUrl":"https://doi.org/10.23952/jnfa.2020.4","url":null,"abstract":". This paper aims at establishing the multiplicity results of nontrivial weak solutions for impulsive elastic beam equations of the Kirchhoff-type. The approach follows variational methods and the critical point theory.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777337","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 this paper, a new iterative algorithm with a self-adaptive step size is proposed for split feasibility problem involving bifunctions and Bregman quasi-nonexpansive mappings. A strong convergence theorem is obtained in the framework of real reflexive Banach spaces. An application and an example are presented to illustrate the performance of our algorithm.
{"title":"A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces","authors":"O. Oyewole, O. Mewomo","doi":"10.23952/jnfa.2020.37","DOIUrl":"https://doi.org/10.23952/jnfa.2020.37","url":null,"abstract":". In this paper, a new iterative algorithm with a self-adaptive step size is proposed for split feasibility problem involving bifunctions and Bregman quasi-nonexpansive mappings. A strong convergence theorem is obtained in the framework of real reflexive Banach spaces. An application and an example are presented to illustrate the performance of our algorithm.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777300","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 this paper, we present a mathematically rigorous analysis for the global asymptotic stability of a recognized SEIRS model with nonlinear incidence and vertical transmission. Our main objective is to re-establish the local asymptotic stability of the disease endemic equilibrium point without the assumption proposed in [L. Qi, J. Cui, The stability of an SEIRS model with nonlinear incidence, vertical transmission and time delay, Appl. Math. Comput. 221 (2013), 360-366] and prove that this equilibrium point is not only locally asymptotically stable but also globally asymptotically stable if it exists. Therefore, the global stability of the model is established rigorously. Additionally, we design nonstandard finite difference (NSFD) schemes that preserve essential properties of the SEIRS model using the Mickens methodology. A set of numerical experiments are performed to support the validity of the theoretical results as well as to show advantages and efficiency of the NSFD schemes over the standard finite difference schemes.
{"title":"Global asymptotic stability of an SEIRS model and its solutions by nonstandard finite difference schemes","authors":"M. T. Hoang, O. Egbelowo","doi":"10.23952/jnfa.2020.34","DOIUrl":"https://doi.org/10.23952/jnfa.2020.34","url":null,"abstract":". In this paper, we present a mathematically rigorous analysis for the global asymptotic stability of a recognized SEIRS model with nonlinear incidence and vertical transmission. Our main objective is to re-establish the local asymptotic stability of the disease endemic equilibrium point without the assumption proposed in [L. Qi, J. Cui, The stability of an SEIRS model with nonlinear incidence, vertical transmission and time delay, Appl. Math. Comput. 221 (2013), 360-366] and prove that this equilibrium point is not only locally asymptotically stable but also globally asymptotically stable if it exists. Therefore, the global stability of the model is established rigorously. Additionally, we design nonstandard finite difference (NSFD) schemes that preserve essential properties of the SEIRS model using the Mickens methodology. A set of numerical experiments are performed to support the validity of the theoretical results as well as to show advantages and efficiency of the NSFD schemes over the standard finite difference schemes.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777594","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 concerned with a general decay synchronization (GDS) between two delayed non-autonomous cellular neural networks. A non-autonomous case and infinite delays are taken into consideration. By using the Lyapunov stability theory and employing useful inequality techniques, some sufficient conditions on the GDS of the considered system are established based on a type of nonlinear control. In addition, an example with numerical simulations is provided to demonstrate the effectiveness and feasibility of the obtained results.
{"title":"Synchronization on the non-autonomous cellular neural networks with time delays","authors":"Azhar Halik, Aishan Wumaier","doi":"10.23952/jnfa.2020.51","DOIUrl":"https://doi.org/10.23952/jnfa.2020.51","url":null,"abstract":". This paper is concerned with a general decay synchronization (GDS) between two delayed non-autonomous cellular neural networks. A non-autonomous case and infinite delays are taken into consideration. By using the Lyapunov stability theory and employing useful inequality techniques, some sufficient conditions on the GDS of the considered system are established based on a type of nonlinear control. In addition, an example with numerical simulations is provided to demonstrate the effectiveness and feasibility of the obtained results.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777612","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 this paper, we consider the following damped vibration system ¨ u ( t )+ q ( t ) ˙ u ( t ) − L ( t ) u ( t )+ ∇ W ( t , u ( t )) = 0 , ∀ t ∈ R , where q ∈ C ( R , R ) , L ∈ C ( R , R N 2 ) is a symmetric matrix valued function and W ( t , x ) ∈ C 1 ( R × R N , R ) . We prove the existence of infinitely many fast homoclinic solutions for the system when Q ( t ) = (cid:82) t 0 q ( s ) ds → + ∞ as | t | → ∞ , L is neither coercive nor uniformly positive definite and W ( t , x ) is superquadratic at infinity in the second variable but does not satisfy the well-known superquadratic growth conditions like the Ambrosetti-Rabinowitz or the Fei’s conditions.
． 在本文中,我们考虑下面的阻尼振动系统¨u (t) + q (t)˙u (t)−L (t) u (t) +∇W (t, u (t)) = 0,∀t∈R, q∈C (R, R), L∈C (R, R N 2)是一个对称矩阵值函数和W C (t) x)∈1 (R×R N, R)。我们证明存在无穷多快类解决方案系统时问(t) = (cid: 82) t 0 Q (s) ds→+∞| | t→∞,L是强制性和均匀正定和W (t, x)超是在第二个变量但无穷满足超有名的生长条件不像范Ambrosetti-Rabinowitz或的条件。
{"title":"Infinitely many fast homoclinic orbits for a class of superquadratic damped vibration systems","authors":"M. Timoumi","doi":"10.23952/jnfa.2020.8","DOIUrl":"https://doi.org/10.23952/jnfa.2020.8","url":null,"abstract":". In this paper, we consider the following damped vibration system ¨ u ( t )+ q ( t ) ˙ u ( t ) − L ( t ) u ( t )+ ∇ W ( t , u ( t )) = 0 , ∀ t ∈ R , where q ∈ C ( R , R ) , L ∈ C ( R , R N 2 ) is a symmetric matrix valued function and W ( t , x ) ∈ C 1 ( R × R N , R ) . We prove the existence of infinitely many fast homoclinic solutions for the system when Q ( t ) = (cid:82) t 0 q ( s ) ds → + ∞ as | t | → ∞ , L is neither coercive nor uniformly positive definite and W ( t , x ) is superquadratic at infinity in the second variable but does not satisfy the well-known superquadratic growth conditions like the Ambrosetti-Rabinowitz or the Fei’s conditions.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777701","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 this article, we prove the existence of entropy solutions for the Dirichlet problem where Ω is a bounded open set of R N , N ≥ 2 and f ∈ L 1 ( Ω ) . An example is provided to support our result.
． 本文证明了Dirichlet问题的熵解的存在性，其中Ω是R N, N≥2,f∈l1 (Ω)的有界开集。给出了一个示例来支持我们的结果。
{"title":"The existence of entropy solutions for nonlinear degenerate elliptic equations","authors":"A. C. Cavalheiro, A. C. Cavalheiro","doi":"10.23952/jnfa.2020.38","DOIUrl":"https://doi.org/10.23952/jnfa.2020.38","url":null,"abstract":". In this article, we prove the existence of entropy solutions for the Dirichlet problem where Ω is a bounded open set of R N , N ≥ 2 and f ∈ L 1 ( Ω ) . An example is provided to support our result.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777317","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 this paper, we investigate the unique existence, general decay and blow-up of solutions of an initial-boundary value problem for a viscoelastic wave equation with Robin-Dirichlet conditions. The proof is based on Faedo-Galerkin method associated with a priori estimate, weak convergence and compactness techniques. A numerical example is also given to illustrate the decay property of the solutions.
{"title":"General decay and blow-up results of solutions for a viscoelastic wave equation with Robin-Dirichlet conditions","authors":"L. Ngoc, L. Tri, LE Tran Ngoc Tran, N. Long","doi":"10.23952/jnfa.2020.42","DOIUrl":"https://doi.org/10.23952/jnfa.2020.42","url":null,"abstract":"In this paper, we investigate the unique existence, general decay and blow-up of solutions of an initial-boundary value problem for a viscoelastic wave equation with Robin-Dirichlet conditions. The proof is based on Faedo-Galerkin method associated with a priori estimate, weak convergence and compactness techniques. A numerical example is also given to illustrate the decay property of the solutions.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777377","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 beam modelled by a Timoshenko system with a viscoelastic damping on one component is considered. The system is coupled with a hyperbolic heat equation. One end of the structure is fixed to a platform in a translational movement and the other one is attached to a non-negligble mass. The well-posedness and asymptotic stability results for the system under some conditions on the initial and the boundary data are established.
{"title":"General stability results for the translational problem of memory-type in porous thermoelasticity of type III","authors":"A. Guesmia, Mohammad M. Kafini, N. Tatar","doi":"10.23952/jnfa.2020.49","DOIUrl":"https://doi.org/10.23952/jnfa.2020.49","url":null,"abstract":". A beam modelled by a Timoshenko system with a viscoelastic damping on one component is considered. The system is coupled with a hyperbolic heat equation. One end of the structure is fixed to a platform in a translational movement and the other one is attached to a non-negligble mass. The well-posedness and asymptotic stability results for the system under some conditions on the initial and the boundary data are established.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777537","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}
For solving monotone variational inequalities and fixed point problems of a quasi-nonexpansive mapping in real Hilbert spaces, we introduce two new algorithms which combine the inertial Tseng’s extragradient method and the hybrid-projection method, respectively. Weak and strong convergence theorems are established under some appropriate conditions. Finally, we provide some numerical experiments to show the effectiveness and advantages of the proposed algorithms.
{"title":"Inertial modified Tseng’s extragradient algorithms for solving monotone variational inequalities and fixed point problems","authors":"M. Tian, XU Gang","doi":"10.23952/jnfa.2020.35","DOIUrl":"https://doi.org/10.23952/jnfa.2020.35","url":null,"abstract":"For solving monotone variational inequalities and fixed point problems of a quasi-nonexpansive mapping in real Hilbert spaces, we introduce two new algorithms which combine the inertial Tseng’s extragradient method and the hybrid-projection method, respectively. Weak and strong convergence theorems are established under some appropriate conditions. Finally, we provide some numerical experiments to show the effectiveness and advantages of the proposed algorithms.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777786","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 this paper, we study the existence and multiplicity of fast homoclinic orbits for the class of damped vibration systems ¨ where L ( t ) is not required to be either uniformly positive definite or coercive, and W ( t , x ) is of subquadratic or superquadratic growth as | x | → ∞ , or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic at infinity). To the best of our knowl-edge, there is no result concerning the existence and multiplicity of homoclinic orbits for the system with the conditions.
． 本文研究了一类阻尼振动系统的快速同斜轨道的存在性和多重性，其中L (t)不要求一致正定或强制，W (t, x)在| x |→∞时是次二次或超二次增长，或仅满足原点附近的局部条件(即在无穷远处可以是次二次、超二次或渐近二次)。据我们所知，对于具有这些条件的系统，没有关于同斜轨道存在性和多重性的结果。
{"title":"Infinitely many fast homoclinic solutions for different classes of damped vibration systems","authors":"M. Timoumi","doi":"10.23952/jnfa.2020.46","DOIUrl":"https://doi.org/10.23952/jnfa.2020.46","url":null,"abstract":". In this paper, we study the existence and multiplicity of fast homoclinic orbits for the class of damped vibration systems ¨ where L ( t ) is not required to be either uniformly positive definite or coercive, and W ( t , x ) is of subquadratic or superquadratic growth as | x | → ∞ , or satisfies only local conditions near the origin (i.e., it can be subquadratic, superquadratic or asymptotically quadratic at infinity). To the best of our knowl-edge, there is no result concerning the existence and multiplicity of homoclinic orbits for the system with the conditions.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68777463","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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