Description

• Title:
  Ground state solutions for a class of semilinear elliptic systems with sum of periodic and vanishing potentials
• Creator:
  Che, Guofeng;
  Chen, Haibo
• Description:
  In this paper, we consider the following semilinear elliptic systems: $$ \begin{cases} -\Delta u+V(x)u=F_{u}(x, u, v)-\Gamma(x)|u|^{q-2}u & \mbox{in }\mathbb{R}^{N},\\ -\Delta v+V(x)v=F_{v}(x, u, v)-\Gamma(x)|v|^{q-2}v & \mbox{in }\mathbb{R}^{N},\\ \end{cases} $$% where $q\in[2,2^{*})$, $V=V_{\rom{per}}+V_{\rom{loc}}\in L^{\infty}(\mathbb{R}^{N})$ is the sum of a periodic potential $V_{\rom{per}}$ and a localized potential $V_{\rom{loc}}$ and $\Gamma\in L^{\infty}(\mathbb{R}^{N})$ is periodic and $\Gamma(x)\geq0$ for almost every $x\in\mathbb{R}^{N}$. Under some appropriate assumptions on $F$, we investigate the existence and nonexistence of ground state solutions for the above system. Recent results from the literature are improved and extended.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.11.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 51, No 1 (March 2018); 215 - 242;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.046/13429 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.046/13430
• Subject:
  Semilinear elliptic systems;
  ground state;
  periodic potential;
  localized potential;
  variational methods;
  35B38;
  35J20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.046
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other