Description

• Title:
  Quasilinear nonhomogeneous Schrödinger equation with critical exponential growth in R^n
• Creator:
  Silva, Tarciana;
  Souza, Manassés de;
  Marcos do Ó, João
• Description:
  In this paper, using variational methods, we establish the existence and multiplicity of weak solutions for nonhomogeneous quasilinear elliptic equations of the form -\Delta_n u + a(x)|u|^{n-2}u= b(x)|u|^{n-2}u+g(x)f(u)+\varepsilon h \quad \mbox{in }\mathbb{R}^n , where $n \geq 2$, $ \Delta_n u \equiv \dive(|\nabla u|^{n-2}\nabla u)$ is the $n$-Laplacian and $\varepsilon$ is a positive parameter. Here the function $g(x)$ may be unbounded in $x$ and the nonlinearity $f(s)$ has critical growth in the sense of Trudinger-Moser inequality, more precisely $f(s)$ behaves like $e^{\alpha_0 |s|^{n/(n-1)}}$ when $s\to+\infty$ for some $\alpha_0>0$. Under some suitable assumptions and based on a Trudinger-Moser type inequality, our results are proved by using Ekeland variational principle, minimization and mountain-pass theorem.
• 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); 615 - 639;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.029/7461
• Subject:
  Variational methods;
  Trudinger-Moser inequality;
  critical points;
  critical exponents;
  $n$-Laplacian;
  35J20;
  35J60;
  35B33
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.029
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other