Description

• Title:
  Uniqueness of positive and compacton-type solutions for a resonant quasilinear problem
• Creator:
  Anello, Giovanni;
  Vilasi, Luca
• Description:
  We study a one-dimensional $p$-Laplacian resonant problem with $p$-sublinear terms and depending on a positive parameter. By using quadrature methods we provide the exact number of positive solutions with respect to $\mu\in\mathopen{]}0,+\infty\mathclose[$. Specifically, we prove the existence of a critical value $\mu_1> 0$ such that the problem under examination admits: no positive solutions and a continuum of nonnegative solutions compactly supported in $[0,1]$ for $\mu\in\mathopen{]}0,\mu_1\mathclose[$; a unique positive solution of compacton-type for $\mu=\mu_1$; a unique positive solution satisfying Hopf's boundary condition for $\mu\in\mathopen{]}\mu_1,+\infty\mathclose[$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.12.28
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 49, No 2 (June 2017); 565 - 575;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.090/10661 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.090/10662
• Subject:
  Quasilinear problem;
  resonant problem;
  positive solution;
  compacton-type solution;
  uniqueness;
  34B08;
  34B15;
  34B18
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.090
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other