Description

• Title:
  Existence and asymptotic behaviour of ground state solutions for quasilinear Schrodinger-Poisson systems in $R^3$
• Creator:
  Ding, Ling;
  Li, Lin;
  Meng, Jixiang;
  Zhu, Chun
• Description:
  In this paper, we are concerned with existence and asymptotic behavior of ground state in the whole space $\mathbb{R}^3$ for quasilinear Schr\"odinger--Poisson systems $$ \begin{cases} -\Delta u+u+K(x)\phi(x)u=a(x)f(u), x\in \mathbb{R}^3, \\ -\mbox{div}[(1+\varepsilon^4|\nabla\phi|^2)\nabla\phi]=K(x)u^2, x\in \mathbb{R}^3, \end{cases} $$ when the nonlinearity coefficient $\varepsilon\ge 0$ goes to zero, where $f(t)$ is asymptotically linear with respect to $t$ at infinity. Under appropriate assumptions on $K$, $a$ and $ f$, we establish existence of a ground state solution $(u_\varepsilon, \phi_{\varepsilon, K}(u_\varepsilon))$ of the above system. Furthermore, for all $\varepsilon$ sufficiently small, we show that $(u_\varepsilon, \phi_{\varepsilon, K}(u_\varepsilon))$ converges to $(u_0, \phi_{0, K}(u_0))$ which is the solution of the corresponding system for $\varepsilon=0$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 47, No 1 (March 2016); 241 - 264;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.004/7601 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.004/7602
• Subject:
  Schrodinger-Poisson system;
  variational methods;
  ground state solution;
  asymptotically linear;
  asymptotic behavior;
  Primary;
  35Q55;
  82D99;
  Secondary;
  35B25;
  35B40;
  35J50;
  47J30;
  58E05;
  81Q05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.004
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other