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Electronic Journal of Differential Equations最新文献

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Existence and decay of solutions to coupled systems of nonlinear wave equations with variable exponents 变指数非线性波动方程耦合系统解的存在性与衰减性
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-24 DOI: 10.58997/ejde.2023.73
Oulia Bouhoufani, Salim A. Messaoudi, Mostafa Zahri
{"title":"Existence and decay of solutions to coupled systems of nonlinear wave equations with variable exponents","authors":"Oulia Bouhoufani, Salim A. Messaoudi, Mostafa Zahri","doi":"10.58997/ejde.2023.73","DOIUrl":"https://doi.org/10.58997/ejde.2023.73","url":null,"abstract":"In this article, we consider a coupled system of two hyperbolic equations with variable exponents in the damping and source terms, where the dampings are modilated with time-dependent coefficients (alpha(t), beta(t)). First, we state and prove an existence result of a global weak solution, using Galerkin's method with compactness arguments. Then, by a Lemma due to Martinez, we establish the decay rates of the solution energy, under suitable assumptions on the variable exponents (m) and (r) and the coefficients ( alpha) and (beta). To illustrate our theoretical results, we give some numerical examples.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/73/abstr.html
","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135315785","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
Qualitative properties of solutions to a reaction-diffusion equation with weighted strong reaction 带加权强反应的反应扩散方程解的定性性质
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-23 DOI: 10.58997/ejde.2023.72
Razvan Gabriel Iagar, Ana I. Munoz, Ariel Sanchez
{"title":"Qualitative properties of solutions to a reaction-diffusion equation with weighted strong reaction","authors":"Razvan Gabriel Iagar, Ana I. Munoz, Ariel Sanchez","doi":"10.58997/ejde.2023.72","DOIUrl":"https://doi.org/10.58997/ejde.2023.72","url":null,"abstract":"We study the existence and qualitative properties of solutions to the Cauchy problem associated to the quasilinear reaction-diffusion equation $$ partial_tu=Delta u^m+(1+|x|)^{sigma}u^p, $$ posed for ((x,t)inmathbb{R}^Ntimes(0,infty)), where (m>1), (pin(0,1)) and (sigma>0). Initial data are taken to be bounded, non-negative and compactly supported. In the range when (m+pgeq2), we prove existence of local solutions with a finite speed of propagation of their supports for compactly supported initial conditions. We also show in this case that, for a given compactly supported initial condition, there exist infinitely many solutions to the Cauchy problem, by prescribing the evolution of their interface. In the complementary range (m+p<2), we obtain new Aronson-Benilan estimates satisfied by solutions to the Cauchy problem, which are of independent interest as a priori bounds for the solutions. We apply these estimates to establish infinite speed of propagation of the supports of solutions if (m+p<2), that is, (u(x,t)>0) for any (xinmathbb{R}^N), (t>0), even in the case when the initial condition (u_0) is compactly supported. For more information see https://ejde.math.txstate.edu/Volumes/2023/72/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135414856","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
G-convergence of elliptic operators in non divergence form in R^n R^n中非发散形式椭圆算子的g收敛性
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-20 DOI: 10.58997/ejde.2023.71
Luigi D'Onofrio
{"title":"G-convergence of elliptic operators in non divergence form in R^n","authors":"Luigi D'Onofrio","doi":"10.58997/ejde.2023.71","DOIUrl":"https://doi.org/10.58997/ejde.2023.71","url":null,"abstract":"The aim of this note is to prove a characterization of the G-limit of a sequence of elliptic operators in non-divergence form. As we consider any dimension, for this class of operators, it is not enough to deal with measurable and bounded coefficients so we need extra regularity assumptions on them.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2023/71/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135618836","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
Lower bounds at infinity for solutions to second order elliptic equations 二阶椭圆方程无穷远处解的下界
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-16 DOI: 10.58997/ejde.2023.69
Tu Nguyen
{"title":"Lower bounds at infinity for solutions to second order elliptic equations","authors":"Tu Nguyen","doi":"10.58997/ejde.2023.69","DOIUrl":"https://doi.org/10.58997/ejde.2023.69","url":null,"abstract":"We study lower bounds at infinity for solutions to $$ |Pu|leq M|x|^{-delta_1}|nabla u|+M|x|^{-delta_{0}}|u| $$ where $P$ is a second order elliptic operator. Our results are of quantitative nature and generalize those obtained in [3,6].&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2023/69/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136142329","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
Oscillation criteria of fourth-order nonlinear semi-noncanonical neutral differential equations via a canonical transform 四阶非线性半非正则中立型微分方程的正则变换振动判据
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-16 DOI: 10.58997/ejde.2023.70
Ganesh Purushothaman, Kannan Suresh, Ercan Tunc, Ethiraju Thandapani
{"title":"Oscillation criteria of fourth-order nonlinear semi-noncanonical neutral differential equations via a canonical transform","authors":"Ganesh Purushothaman, Kannan Suresh, Ercan Tunc, Ethiraju Thandapani","doi":"10.58997/ejde.2023.70","DOIUrl":"https://doi.org/10.58997/ejde.2023.70","url":null,"abstract":"In this work first we transform the semi-noncanonical fourth order neutral delay differential equations into canonical type. This simplifies the investigations of finding the relationships between the solution and its companion function which plays an important role in the oscillation theory of neutral differential equations. Moreover, we improve these relationships based on the monotonic properties of positive solutions. We present new conditions for the oscillation of all solutions of the corresponding equation which improve the oscillation results already reported in the literature. Examples are provided to illustrate the importance of our main results. For moreinformation see https://ejde.math.txstate.edu/Volumes/2023/70/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136142332","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
Stability and instability of Kirchhoff plate equations with delay on the boundary control 边界控制下具有时滞的Kirchhoff板方程的稳定性和不稳定性
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-16 DOI: 10.58997/ejde.2023.68
Haidar Badawi, Mohammad Akil, Zayd Hajjej
{"title":"Stability and instability of Kirchhoff plate equations with delay on the boundary control","authors":"Haidar Badawi, Mohammad Akil, Zayd Hajjej","doi":"10.58997/ejde.2023.68","DOIUrl":"https://doi.org/10.58997/ejde.2023.68","url":null,"abstract":"In this article, we consider the Kirchhoff plate equation with delay terms on the boundary control. We give instability examples of systems for some choices of delays. Finally, we prove its well-posedness, strong stability, and exponential stability under a multiplier geometric control condition.&#x0D; Foro more information see https://ejde.math.txstate.edu/Volumes/2023/68/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136142208","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
Boundedness on generalized Morrey spaces for the Schrodinger operator with potential in a reverse Holder class 逆Holder类中具有势的薛定谔算子广义Morrey空间上的有界性
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-13 DOI: 10.58997/ejde.2023.67
Guiyun Wang, Shenzhou Zheng
{"title":"Boundedness on generalized Morrey spaces for the Schrodinger operator with potential in a reverse Holder class","authors":"Guiyun Wang, Shenzhou Zheng","doi":"10.58997/ejde.2023.67","DOIUrl":"https://doi.org/10.58997/ejde.2023.67","url":null,"abstract":"In this article, we prove boundedness for the Hessian of a Schrodinger operator with weak regularity on the coefficients, and potentials satisfying the reverse H\"older condition. This is done in in generalized Morrey spaces, and in vanishing generalized Morrey spaces. On the Schrodinger operator (L=-a_{ij}(x)D_{ij}+V(x)) it is assumed that (a_{ij}in rm{BMO}_{theta}(rho)) (a generalized Morrey space) and that (V(x)in B^*_{n/2}) (a reverse Holder class).&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2023/67/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918286","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 and asymptotic behavior of solutions to eigenvalue problems for Schrodinger-Bopp-Podolsky equations 薛定谔-波普-波多尔斯基方程特征值问题解的存在性和渐近性
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-13 DOI: 10.58997/ejde.2023.66
Lorena Soriano Hernandez, Gaetano Siciliano
{"title":"Existence and asymptotic behavior of solutions to eigenvalue problems for Schrodinger-Bopp-Podolsky equations","authors":"Lorena Soriano Hernandez, Gaetano Siciliano","doi":"10.58997/ejde.2023.66","DOIUrl":"https://doi.org/10.58997/ejde.2023.66","url":null,"abstract":"We study the existence and multiplicity of solutions for the Schrodinger-Bopp-Podolsky system $$displaylines{ -Delta u + phi u = omega u quadtext{ in } Omega cr a^2Delta^2phi-Delta phi = u^2 quadtext{ in } Omega cr u=phi=Deltaphi=0quadtext{ on } partialOmega cr int_{Omega} u^2,dx =1 }$$ where (Omega) is an open bounded and smooth domain in (mathbb R^{3}), (a&gt;0 ) is the Bopp-Podolsky parameter. The unknowns are (u,phi:Omegato mathbb R) and (omegainmathbb R). By using variational methods we show that for any (a&gt;0) there are infinitely many solutions with diverging energy and divergent in norm. We show that ground states solutions converge to a ground state solution of the related classical Schrodinger-Poisson system, as (ato 0). For more information see https://ejde.math.txstate.edu/Volumes/2023/66/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918943","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: 1
Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term 具有变符号强迫项的非自治Duffing方程的参数相关周期问题
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-10-05 DOI: 10.58997/ejde.2023.65
Jiri Sremr
{"title":"Parameter-dependent periodic problems for non-autonomous Duffing equations with sign-changing forcing term","authors":"Jiri Sremr","doi":"10.58997/ejde.2023.65","DOIUrl":"https://doi.org/10.58997/ejde.2023.65","url":null,"abstract":"We study the existence, exact multiplicity, and structure of the set of positive solutions to the periodic problem $$ u''=p(t)u+h(t)|u|^{lambda}operatorname{sgn} u+mu f(t);quad u(0)=u(omega),; u'(0)=u'(omega), $$ where (muin mathbb{R}) is a parameter. We assume that (p,h,fin L([0,omega])), (lambda&gt;1), and the function (h) is non-negative. The results obtained extend the results known in the existing literature. We do not require that the Green's function of the corresponding linear problem be positive and we allow the forcing term (f) to change its sign.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2023/65/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135546506","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
Local well-posedness and standing waves with prescribed mass for Schrodinger-Poisson systems with a logarithmic potential in R^2 具有R^2对数势的薛定谔-泊松系统的局部适定性和规定质量的驻波
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-09-25 DOI: 10.58997/ejde.2023.64
Xuechao Dou, Juntao Sun
{"title":"Local well-posedness and standing waves with prescribed mass for Schrodinger-Poisson systems with a logarithmic potential in R^2","authors":"Xuechao Dou, Juntao Sun","doi":"10.58997/ejde.2023.64","DOIUrl":"https://doi.org/10.58997/ejde.2023.64","url":null,"abstract":"In this article, we consider planar Schrodinger-Poisson systems with a logarithmic external potential (W(x)=ln (1+|x|^2)) and a general nonlinear term (f). We obtain conditions for the local well-posedness of the Cauchy problem in the energy space. By introducing some suitable assumptions on (f), we prove the existence of the global minimizer. In addition, with the help of the local well-posedness, we show that the set of ground state standing waves is orbitally stable.&#x0D; For more information see https://ejde.math.txstate.edu/Volumes/2023/64/abstr.html&#x0D;","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135864035","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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