Description

• Title:
  Hénon type equations with one-sided exponential growth
• Creator:
  do Ó, João Marcos;
  Barboza, Eudes Mendes;
  Ribeiro, Bruno
• Description:
  We deal with the following class of problems: \begin{equation*} \begin{cases} -\Delta u=\lambda u+|x|^{\alpha}g(u_+)+ f(x)&\mbox{in } B_1,\\ u =0&\mbox{on }\partial B_1, \end{cases} \end{equation*} where $B_1$ is the unit ball in $\mathbb R^2$, $g$ is a $C^1$-function in $[0,+\infty)$ which is assumed to be in the subcritical or critical growth range of Trudinger-Moser type and $f\in L^{\mu}(B_1)$ for some $\mu> 2$. Under suitable hypotheses on the constant $\lambda$, we prove existence of at least two solutions to this problem using variational methods. In case of $f$ radially symmetric, the two solutions are radially symmetric as well.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Date:
  2017.05.22
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 49, No 2 (June 2017); 783 - 816;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.010/12126 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.010/12127
• Subject:
  Hénon type equation;
  Ambrosetti-Prodi problem;
  critical growth;
  Primary;
  35J20;
  35J25;
  Secondary;
  47J30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.010
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other