Description

• Title:
  Neumann problems with double resonance
• Creator:
  O'Regan, Donal;
  Papageorgiou, Nikolaos S.;
  Smyrlis, George
• Description:
  We study elliptic Neumann problems in which the reaction term at infinity is resonant with respect to any pair $\{ \widehat{\lambda}_m, \widehat{\lambda}_{m+1}\}$ of distinct consecutive eigenvalues. Using variational methods combined with Morse theoretic techniques, we show that when the double resonance occurs in a ``nonprincipal'' spectral interval $[\widehat{\lambda}_m, \widehat{\lambda}_{m+1}]$, $ m\geq 1$, we have at least three nontrivial smooth solutions, two of which have constant sign. If the double resonance occurs in the ``principal'' spectral $[\widehat{\lambda}_0=0,\widehat{\lambda}_1]$, then we show that the problem has at least one nontrivial smooth solution.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2012.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 39, No 1 (March 2012); 151 - 173;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.009/8359
• Subject:
  Double resonance;
  C-condition;
  unique continuation property;
  critical groups;
  Morse theory;
  homotopy invariance;
  35J80;
  35J85;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.009
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other