Description

• Title:
  Solutions to a nonlinear Schrödinger equation with periodic potential and zero on the boundary of the spectrum
• Creator:
  Mederski, Jarosław
• Description:
  We study the following nonlinear Schrodinger equation\begin{equation*}\begin{cases}  -\Delta u + V(x) u = g(x,u)  &  \hbox{for } x\in\R^N,\\  u(x)\to 0  &  \hbox{as } |x|\to\infty,\end{cases}\end{equation*}where $V\colon \R^N\to\R$ and $g\colon \R^N\times\R\to\R$ are periodic in $x$. We assume that $0$ is a right boundary point of the essential spectrum of $-\Delta+V$. The superlinear and subcritical term g satisfies a Nehari type monotonicity condition. We employ a Nehari manifold type technique in a strongly indefitnite setting and obtain the existence of a ground state solution. Moreover, we get infinitely many geometrically distinct solutions provided that $g$ is odd.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 755 - 772;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.067/7263 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.067/7300
• Subject:
  Schrodinger equation;
  ground state;
  variational methods;
  strongly indefinite functional;
  Nehari-Pankov manifold;
  Primary 35Q55;
  Secondary 35J10;
  35J20;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.067
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other