Description

• Title:
  Existence and multiplicity results for semilinear ellipctic equations with measure data and jumping nonlinearities
• Creator:
  Ferrero, Alberto;
  Saccon, Claudio
• Description:
  We study existence and multiplicity results for semilinear elliptic equations of the type $-\Delta u=g(x,u)-te_1+\mu$ with homogeneous Dirichlet boundary conditions. Here $g(x,u)$ is a jumping nonlinearity, $\mu$ is a Radon measure, $t$ is a positive constant and $e_1> 0$ is the first eigenfunction of $-\Delta$. Existence results strictly depend on the asymptotic behavior of $g(x,u)$ as $u\rightarrow\pm \infty$. Depending on this asymptotic behavior, we prove existence of two and three solutions for $t> 0$ large enough. In order to find solutions of the equation, we introduce a suitable action functional $I_t$ by mean of an appropriate iterative scheme. Then we apply to $I_t$ standard results from the critical point theory and we prove existence of critical points for this functional.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2007.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 30, No 1 (September 2007); 37 - 65;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.018/8837
• Subject:
  Semilinear equations;
  Radon measures;
  critical point theory;
  35A15;
  35J25;
  35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2007.018
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other