{"title":"Caratheodory periodic perturbations of degenerate systems","authors":"A. Calamai, M. Spadini","doi":"10.58997/ejde.2024.39","DOIUrl":"https://doi.org/10.58997/ejde.2024.39","url":null,"abstract":"We study the structure of the set of harmonic solutions to T-periodically perturbed coupled differential equations on differentiable manifolds, where the perturbation is allowed to be of Caratheodory-type regularity. Employing degree-theoretic methods, we prove the existence of a noncompact connected set of nontrivial T-periodic solutions that, in a sense, emanates from the set of zeros of the unperturbed vector field. The latter is assumed to be ''degenerate'': Meaning that, contrary to the usual assumptions on the leading vector field, it is not required to be either trivial nor to have a compact set of zeros. In fact, known results in the ``nondegenerate case can be recovered from our ones. We also provide some illustrating examples of Lienard- and (phi)-Laplacian-type perturbed equations.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/39/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141666469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A second order convergent difference scheme for the initial-boundary value problem of Rosenau-Burgers equation","authors":"Sitong Dong, Xin Zhang, Yuanfeng Jin","doi":"10.58997/ejde.2024.38","DOIUrl":"https://doi.org/10.58997/ejde.2024.38","url":null,"abstract":"We construct a two-level implicit nonlinear finite difference scheme for the initial boundary value problem of Rosenau-Burgers equation based on the method of order reduction. We discuss conservation, unique solvability, and convergence for the difference scheme. The new scheme is shown to be second-order convergent in time and space. Finally, numerical simulations illustrate our theoretical analysis.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/38/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Massera type theorems for abstract non-autonomous evolution equations","authors":"Lan-Ling Zheng, Hui-Sheng Ding","doi":"10.58997/35","DOIUrl":"https://doi.org/10.58997/35","url":null,"abstract":"We establish two fixed point theorems for affine maps in Banach spaces, with weaker assumptions than those in the literature. Then we establish some Massera type results for abstract linear evolution equations without assuming the existence of bounded solutions, which is an indispensable condition in the classical Massera theorem and in the earlier literature. As application, we present an existence result on periodic mild solutions to abstract nonautonomous semilinear evolution equations. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/35/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141376754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joao Pablo Pinheiro da Silva, Edcarlos Domingos da Silva
{"title":"Existence of semi-nodal solutions for elliptic systems related to Gross-Pitaevskii equations","authors":"Joao Pablo Pinheiro da Silva, Edcarlos Domingos da Silva","doi":"10.58997/ejde.2024.32","DOIUrl":"https://doi.org/10.58997/ejde.2024.32","url":null,"abstract":"In this work we consider existence of semi-nodal solutions, i.e., solutions of the form ((u, v)) with (u>0) and (v^pm:=max{0,pm v}notequiv0) for a class of elliptic systems related to the Gross-Pitaevskii equation. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/32/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140656852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nodal solutions for nonlinear Schrodinger systems","authors":"Xue Zhou, Xiangqing Liu","doi":"10.58997/ejde.2024.31","DOIUrl":"https://doi.org/10.58997/ejde.2024.31","url":null,"abstract":"In this article we consider the nonlinear Schrodinger system $$displaylines{ - Delta u_j + lambda_j u_j = sum_{i=1}^k beta_{ij} u_i^2 u_j, quad hbox{in } Omega, cr u_j ( x ) = 0,quad hbox{on } partial Omega , ; j=1,ldots,k , }$$ where (Omegasubset mathbb{R}^N ) ((N=2,3)) is a bounded smooth domain, (lambda_j> 0), (j=1,ldots,k), (beta_{ij}) are constants satisfying (beta_{jj}>0), (beta_{ij}=beta_{ji}leq 0 ) for (1leq i< jleq k). The existence of sign-changing solutions is proved by the truncation method and the invariant sets of descending flow method. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/31/abstr.html \u0000 ","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140659417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Properties of the solutions to periodic conformable non-autonomous non-instantaneous impulsive differential equations","authors":"Yuanlin Ding, Kui Liu","doi":"10.58997/ejde.2024.30","DOIUrl":"https://doi.org/10.58997/ejde.2024.30","url":null,"abstract":"In this article, we study properties of the solutions to periodic non-autonomous conformable non-instantaneous impulsive differential equations. We use a conformable Cauchy matrix and obtain some basic properties of the periodic solution to the homogeneous and non=homogeneous problems. We consider the periodicity of solutions to nonlinear problem via a fixed theorem.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/30/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140701445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Normalized ground state of a mixed dispersion nonlinear Schrodinger equation with combined power-type nonlinearities","authors":"Zhouji Ma, Xiaojun Chang, Zhaosheng Feng","doi":"10.58997/ejde.2024.29","DOIUrl":"https://doi.org/10.58997/ejde.2024.29","url":null,"abstract":"We study the existence of normalized ground state solutions to a mixed dispersion fourth-order nonlinear Schrodinger equation with combined power-type nonlinearities. By analyzing the subadditivity of the ground state energy with respect to the prescribed mass, we employ a constrained minimization method to establish the existence of ground state that corresponds to a local minimum of the associated functional. Under certain conditions, by studying the monotonicity of ground state energy as the mass varies, we apply the constrained minimization arguments on the Nehari-Pohozaev manifold to prove the existence of normalized ground state solutions. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/29/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140783380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Solutions of linear and non-linear partial differential equations by means of tensor product theory of Banach space","authors":"W. Alshanti","doi":"10.58997/ejde.2024.28","DOIUrl":"https://doi.org/10.58997/ejde.2024.28","url":null,"abstract":"In this article, we introduce an analytical method for solving both non-separable linear and non-linear partial differential equations, for which separation of variables method does not work. This method is based on the theory of tensor product in Banach spaces coupled with some properties of atoms operators. We provide some illustrative examples. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/28/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Existence of solutions to stochastic p(t,x)-Laplace equations and applications","authors":"Chen Liang, Lixu Yan, Yongqiang Fu","doi":"10.58997/ejde.2024.27","DOIUrl":"https://doi.org/10.58997/ejde.2024.27","url":null,"abstract":"In this article, we consider a stochastic $p(t,x)$-Laplace equation. First we use the Galerkin method to obtain a unique weak solution. Then we obtain optimal controls for the corresponding stochastic optimal control problem\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/27/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140376206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Entire solutions to Fermat-type difference and partial differential-difference equations in C^n","authors":"Hong Yan Xu, Goutam Haldar","doi":"10.58997/ejde.2024.26","DOIUrl":"https://doi.org/10.58997/ejde.2024.26","url":null,"abstract":"In this article, we study the existence and the form of finite order transcendental entire solutions of systems of Fermat-type difference and partial differential-difference equations in several complex variables. Our results extend previous theorems given by Xu-Cao [49], Xu et al [52], and Zheng-Xu [55]. We give some examples to illustrate the content of this article.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/26/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140383055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}