Description

• Title:
  Multiple solutions for perturbed quasilinear elliptic problems
• Creator:
  Bartolo, Rossella;
  Candela, Anna Maria;
  Salvatore, Addolorata
• Description:
  We investigate the existence of multiple solutions for the $(p,q)$-quasilinear elliptic problem \[ \begin{cases} -\Delta_p u -\Delta_q u\ =\ g(x, u) + \varepsilon\ h(x,u) & \mbox{in } \Omega,\\ u=0 & \mbox{on } \partial\Omega,\\ \end{cases} \] where $1< p< q< +\infty$, $\Omega$ is an open bounded domain of ${\mathbb R}^N$, the nonlinearity $g(x,u)$ behaves at infinity as $|u|^{q-1}$, $\varepsilon\in{\mathbb R}$ and $h\in C(\overline\Omega\times{\mathbb R},{\mathbb R})$. In spite of the possible lack of a variational structure of this problem, from suitable assumptions on $g(x,u)$ and appropriate procedures and estimates, the existence of multiple solutions can be proved for small perturbations.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Rossella Bartolo, Anna Maria Candela, Addolorata Salvatore
• Date:
  2023.02.26
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 61, No 1 (March 2023); 549 - 574;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/42827/34996 ;https://apcz.umk.pl/TMNA/article/view/42827/34997
• Subject:
  $(p;
  q)$-quasilinear elliptic equation;
  asymptotically $(q-1)$-linear problem;
  q)$-Laplacian operator;
  variational methods;
  essential value;
  perturbed problem;
  pseudo-genus;
  quasi-eigenvalue;
  regularity of solutions;
  Primary: 35J92;
  Secondary: 47J30, 58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/42827
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other