Description

• Title:
  Weak solutions of quasilinear elliptic eystems via the cohomological index
• Creator:
  Candela, Anna Maria;
  de Medeiros, Everaldo Souto;
  Palmieri, Giuliana;
  Perera, Kanishka
• Description:
  In this paper we study a class of quasilinear elliptic systems of the type $$ \cases -\divg(a_1(x,\nabla u_1,\nabla u_2))=f_1(x,u_1,u_2) & \text{in } \Omega,\\ -\divg(a_2(x,\nabla u_1,\nabla u_2))=f_2(x,u_1,u_2) & \text{in } \Omega,\\ u_1 = u_2 = 0 & \text{on } \partial \Omega, \endcases $$ with $\Omega$ bounded domain in $\R^N$. We assume that $A\colon \Omega \times {\mathbb{R}}^N\times{\mathbb{R}}^N\rightarrow{\mathbb{R}}$, $F\colon \Omega \times {\mathbb{R}} \times {\mathbb{R}} \rightarrow {\mathbb{R}}$ exist such that $a=(a_1,a_2)=\nabla A$ satisfies the so called Leray-Lions conditions and $f_1={\partial F}/{\partial u_1}$, $f_2={\partial F}/{\partial u_2}$ are Carathéodory functions with {\it subcritical growth}. The approach relies on variational methods and, in particular, on a cohomological local splitting which allows one to prove the existence of a nontrivial solution.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 36, No 1 (September 2010); 1 - 18;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.024/8447
• Subject:
  Quasilinear elliptic system;
  Leray-Lions conditions;
  subcritical growth;
  cohomological index;
  variational approach;
  p-Laplacian operator;
  35J50;
  35J92;
  47J10;
  47J30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.024
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other