Description

• Title:
  Multiplicity theorems for resonant and superlinear nonhomogeneous elliptic equations
• Creator:
  Papageorgiou, Nikolaos S.;
  Rădulescu, Vicenţiu D.
• Description:
  We consider nonlinear elliptic equations driven by the sum of a $p$-Laplacian ($p> 2$) and a Laplacian. We consider two distinct cases. In the first one, the reaction $f(z,\cdot)$ is $(p-1)$-linear near $\pm\infty$ and resonant with respect to a nonprincipal variational eigenvalue of $(-\Delta_{p},W_{0}^{1,p}(\Omega))$. We prove a multiplicity theorem producing three nontrivial solutions. In the second case, the reaction $f(z,\cdot)$ is $(p-1)$-superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. We prove two multiplicity theorems. In the first main result we produce six nontrivial solutions all with sign information and in the second theorem we have five nontrivial solutions. Our approach uses variational methods combined with the Morse theory, truncation methods, and comparison techniques.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.07.06
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 48, No 1 (September 2016); 283 - 320;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.048/9323 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.048/9324
• Subject:
  Resonance;
  multiple solution;
  superlinear reaction;
  nodal solutions;
  critical groups;
  Primary;
  35J20;
  Secondary;
  35J60;
  35J92;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.048
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other