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Electronic Journal of Differential Equations最新文献

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Uniform attractors of non-autonomous suspension bridge equations with memory 有记忆的非自主悬索桥方程的均匀吸引子
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-02-10 DOI: 10.58997/ejde.2024.16
Lulu Wang, Qiaozhen Ma
{"title":"Uniform attractors of non-autonomous suspension bridge equations with memory","authors":"Lulu Wang, Qiaozhen Ma","doi":"10.58997/ejde.2024.16","DOIUrl":"https://doi.org/10.58997/ejde.2024.16","url":null,"abstract":"In this article, we investigate the long-time dynamical behavior of non-autonomous suspension bridge equations with memory and free boundary conditions. We first establish the well-posedness of the system by means of the maximal monotone operator theory. Secondly, the existence of uniformly bounded absorbing set is obtained. Finally, asymptotic compactness of the process is verified, and then the existence of uniform attractors is proved for non-autonomous suspension bridge equations with memory term.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/16/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139847321","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}
引用次数: 0
Uniform attractors of non-autonomous suspension bridge equations with memory 有记忆的非自主悬索桥方程的均匀吸引子
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-02-10 DOI: 10.58997/ejde.2024.16
Lulu Wang, Qiaozhen Ma
{"title":"Uniform attractors of non-autonomous suspension bridge equations with memory","authors":"Lulu Wang, Qiaozhen Ma","doi":"10.58997/ejde.2024.16","DOIUrl":"https://doi.org/10.58997/ejde.2024.16","url":null,"abstract":"In this article, we investigate the long-time dynamical behavior of non-autonomous suspension bridge equations with memory and free boundary conditions. We first establish the well-posedness of the system by means of the maximal monotone operator theory. Secondly, the existence of uniformly bounded absorbing set is obtained. Finally, asymptotic compactness of the process is verified, and then the existence of uniform attractors is proved for non-autonomous suspension bridge equations with memory term.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/16/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139787503","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}
引用次数: 0
biharmonic equation with discontinuous nonlinearities 不连续非线性双谐波方程
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-02-06 DOI: 10.58997/ejde.2024.15
Eduardo Arias, Marco Calahorrano, Alfonso Castro
{"title":"biharmonic equation with discontinuous nonlinearities","authors":"Eduardo Arias, Marco Calahorrano, Alfonso Castro","doi":"10.58997/ejde.2024.15","DOIUrl":"https://doi.org/10.58997/ejde.2024.15","url":null,"abstract":"We study the biharmonic equation with discontinuous nonlinearity and homogeneous Dirichlet type boundary conditions $$displaylines{ Delta^2u=H(u-a)q(u) quad hbox{in }Omega,cr u=0 quad hbox{on }partialOmega,cr frac{partial u}{partial n}=0 quad hbox{on }partialOmega, }$$ where (Delta) is the Laplace operator, (a> 0), (H) denotes the Heaviside function, (q) is a continuous function, and (Omega) is a domain in (R^N ) with (Ngeq 3). Adapting the method introduced by Ambrosetti and Badiale (The Dual Variational Principle), which is a modification of Clarke and Ekeland's Dual Action Principle, we prove the existence of nontrivial solutions. This method provides a differentiable functional whose critical points yield solutions despite the discontinuity of (H(s-a)q(s)) at (s=a). Considering (Omega) of class (mathcal{C}^{4,gamma}) for some (gammain(0,1)), and the function (q) constrained under certain conditions, we show the existence of two non-trivial solutions. Furthermore, we prove that the free boundary set (Omega_a={xinOmega:u(x)=a}) for the solution obtained through the minimizer has measure zero.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/15/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139860178","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}
引用次数: 0
biharmonic equation with discontinuous nonlinearities 不连续非线性双谐波方程
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-02-06 DOI: 10.58997/ejde.2024.15
Eduardo Arias, Marco Calahorrano, Alfonso Castro
{"title":"biharmonic equation with discontinuous nonlinearities","authors":"Eduardo Arias, Marco Calahorrano, Alfonso Castro","doi":"10.58997/ejde.2024.15","DOIUrl":"https://doi.org/10.58997/ejde.2024.15","url":null,"abstract":"We study the biharmonic equation with discontinuous nonlinearity and homogeneous Dirichlet type boundary conditions $$displaylines{ Delta^2u=H(u-a)q(u) quad hbox{in }Omega,cr u=0 quad hbox{on }partialOmega,cr frac{partial u}{partial n}=0 quad hbox{on }partialOmega, }$$ where (Delta) is the Laplace operator, (a> 0), (H) denotes the Heaviside function, (q) is a continuous function, and (Omega) is a domain in (R^N ) with (Ngeq 3). Adapting the method introduced by Ambrosetti and Badiale (The Dual Variational Principle), which is a modification of Clarke and Ekeland's Dual Action Principle, we prove the existence of nontrivial solutions. This method provides a differentiable functional whose critical points yield solutions despite the discontinuity of (H(s-a)q(s)) at (s=a). Considering (Omega) of class (mathcal{C}^{4,gamma}) for some (gammain(0,1)), and the function (q) constrained under certain conditions, we show the existence of two non-trivial solutions. Furthermore, we prove that the free boundary set (Omega_a={xinOmega:u(x)=a}) for the solution obtained through the minimizer has measure zero.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/15/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139800227","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}
引用次数: 0
Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity 具有指数非线性的准线性薛定谔方程的解的存在性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-02-05 DOI: 10.58997/ejde.2024.14
U. Severo, Bruno H. C. Ribeiro, Diogo de S. Germano
{"title":"Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity","authors":"U. Severo, Bruno H. C. Ribeiro, Diogo de S. Germano","doi":"10.58997/ejde.2024.14","DOIUrl":"https://doi.org/10.58997/ejde.2024.14","url":null,"abstract":"In this article we study the existence of solutions to quasilinear Schrodinger equations in the plane, involving a potential that can change sign and a nonlinear term that may be discontinuous and exhibit exponential critical growth. To prove our existence result, we combine the Trudinger-Moser inequality with a fixed point theorem.\u0000For mote information see https://ejde.math.txstate.edu/Volumes/2024/14/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139802917","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}
引用次数: 0
Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity 具有指数非线性的准线性薛定谔方程的解的存在性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-02-05 DOI: 10.58997/ejde.2024.14
U. Severo, Bruno H. C. Ribeiro, Diogo de S. Germano
{"title":"Existence of solutions to quasilinear Schrodinger equations with exponential nonlinearity","authors":"U. Severo, Bruno H. C. Ribeiro, Diogo de S. Germano","doi":"10.58997/ejde.2024.14","DOIUrl":"https://doi.org/10.58997/ejde.2024.14","url":null,"abstract":"In this article we study the existence of solutions to quasilinear Schrodinger equations in the plane, involving a potential that can change sign and a nonlinear term that may be discontinuous and exhibit exponential critical growth. To prove our existence result, we combine the Trudinger-Moser inequality with a fixed point theorem.\u0000For mote information see https://ejde.math.txstate.edu/Volumes/2024/14/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139862946","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}
引用次数: 0
Global attractor and l^p solutions to initial value problems of discrete nonlinear Schrodinger equations complex potential 离散非线性薛定谔方程复势初值问题的全局吸引子和 l^p 解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-31 DOI: 10.58997/ejde.2024.12
Guoping Zhang, Ghder Aburamyah
{"title":"Global attractor and l^p solutions to initial value problems of discrete nonlinear Schrodinger equations complex potential","authors":"Guoping Zhang, Ghder Aburamyah","doi":"10.58997/ejde.2024.12","DOIUrl":"https://doi.org/10.58997/ejde.2024.12","url":null,"abstract":"In this article, we investigate the global well-posedness of initial value problems of the time-dependent discrete nonlinear Schrodinger equation with a complex potential and sufficiently general nonlinearity on a multidimensional lattice in weighted ( l^p) spaces for ( 1< p <infty). Thanks to our improved estimates we are able to prove the existence of global attractor for ( l^p) solutions to the initial value problem. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/12/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140473379","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}
引用次数: 0
Dirichlet problems with anisotropic principal part involving unbounded coefficients 各向异性主部涉及无约束系数的德里赫特问题
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-30 DOI: 10.58997/ejde.2024.11
D. Motreanu, E. Tornatore
{"title":"Dirichlet problems with anisotropic principal part involving unbounded coefficients","authors":"D. Motreanu, E. Tornatore","doi":"10.58997/ejde.2024.11","DOIUrl":"https://doi.org/10.58997/ejde.2024.11","url":null,"abstract":"This article establishes the existence of solutions in a weak sense for a quasilinear Dirichlet problem exhibiting anisotropic differential operator with unbounded coefficients in the principal part and full dependence on the gradient in the lower order terms. A major part of this work focuses on the existence of a uniform bound for the solution set in the anisotropic setting. The unbounded coefficients are handled through an appropriate truncation and a priori estimates.\u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/11/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140482677","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}
引用次数: 2
Ground state solutions for fractional Kirchhoff type equations with critical growth 具有临界增长的分数基尔霍夫型方程的基态解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-29 DOI: 10.58997/ejde.2024.10
Kexue Li
{"title":"Ground state solutions for fractional Kirchhoff type equations with critical growth","authors":"Kexue Li","doi":"10.58997/ejde.2024.10","DOIUrl":"https://doi.org/10.58997/ejde.2024.10","url":null,"abstract":"We study the nonlinear fractional Kirchhoff problem $$ Big(a+bint_{mathbb{R}^3}|(-Delta)^{s/2}u|^2dxBig) (-Delta)^su+u=f(x,u)+|u|^{2_s^{ast}-2}u quad text{in }mathbb{R}^3, $$ $$ uin H^s(mathbb{R}^3), $$ where (a,b>0) are constants, (s(3/4,1)), (2_s^{ast}=6/(3-2s)), ((-Delta)^s) is the fractional Laplacian. Under some relaxed assumptions on (f), we prove the existence of ground state solutions. \u0000For more inofrmation see https://ejde.math.txstate.edu/Volumes/2024/10/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140489684","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}
引用次数: 0
Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two 特征值乘数为 2 的情况下存在的必要条件和充分条件
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2024-01-24 DOI: 10.58997/ejde.2024.09
Philip Korman
{"title":"Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two","authors":"Philip Korman","doi":"10.58997/ejde.2024.09","DOIUrl":"https://doi.org/10.58997/ejde.2024.09","url":null,"abstract":"We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for unboundness of all solutions of the corresponding semilinear heat equation. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2024/09/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139601606","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}
引用次数: 0
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