Description

• Title:
  Positive solutions to p-Laplace reaction-diffusion systems with nonpositive right-hand side
• Creator:
  Maciejewski, Mateusz
• Description:
  The aim of the paper is to show the existence of positive solutions to the elliptic system of partial differential equations involving the $p$-Laplace operator\[\begin{cases}-\Delta_p u_i(x) = f_i(u_1 (x),u_2(x),\ldots,u_m(x)), & x\in \Omega,\ 1\leq i\leq m,\\u_i(x)\geq 0, & x\in \Omega,\ 1\leq i\leq m,\\u(x) = 0, & x\in \partial \Omega.\end{cases}\]We consider the case of nonpositive right-hand side $f_i$, $i=1,\ldots,m$. The sufficient conditions entails spectral bounds of the matrices associated with $f=(f_1,\ldots,f_m)$. We employ the degree theory from \cite{CwMac} for tangent perturbations of maximal monotone operators in Banach spaces.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 731 - 754;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.065/7262 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.065/7299
• Subject:
  degree theory;
  tangency condition;
  cone;
  quasilinear elliptic system;
  positive weak solution;
  Primary;
  35J57;
  Secondary;
  35B09;
  35D30;
  35J92;
  47H10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.065
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other