Description

• Title:
  Standing waves for nonlinear Schrödinger-Poisson equation with high frequency
• Creator:
  Wang, Zhengping;
  Zhang, Xiaoju;
  Chen, Jianqing
• Description:
  We study the existence of ground state andbound state for the following Schrödinger-Poisson equationwhere $p\in(3,5)$, $\lambda > 0$, $V\inC(\mathbb{R}^3,\mathbb{R}^+)$ and $\lim\limits_{|x|\to+\infty}V(x)=\infty$. By using  variational method, we prove thatfor any $\lambda > 0$, there exists $\delta_1(\lambda) > 0$ such thatfor $\mu_1 < \mu < \mu_1 + \delta_1(\lambda)$, problem (P) has  a nonnegativeground state with negative energy, which bifurcates from zero solution; problem (P) has a nonnegative bound state withpositive energy, which can not bifurcate from zero solution. Here $\mu_1$ is the first eigenvalue of $-\Delta+V$. Infinitely many nontrivial bound states are also obtained withthe help of a generalized version of symmetric mountain passtheorem.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 45, No 2 (June 2015); 601 - 614;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.028/7460
• Subject:
  Schrödinger-Poisson equation;
  ground states;
  bound states;
  variational method;
  Primary 35J20;
  35J70
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.028
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other