Description

• Title:
  Three solutions for a Neumann problem
• Creator:
  Ricceri, Biagio
• Description:
  In this paper we consider a Neumann problem of the type $$ \cases -\Delta u = \alpha (x) (\vert u\vert^{q-2}u-u)+\lambda f(x,u) &\text{in } \Omega, \\ \displaystyle {\partial u\over \partial \nu}=0&\text{on } \partial\Omega. \endcases \tag \hbox{$\text{\rm P}_{\lambda}$} $$ Applying the theory developed in [< i> On a three critical points theorem< /i> , Arch. Math. (Basel) < b> 75< /b> (2000), 220–226], we establish, under suitable assumptions, the existence of an open interval $\Lambda\subseteq \mathbb R$ and of a positive real number $\varrho$, such that, for each $\lambda\in\Lambda$, problem (P$_{\lambda}$) admits at least three weak solutions in $W^{1,2}(\Omega)$ whose norms are less than $\varrho$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2002.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 20, No 2 (December 2002); 275 - 281;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.037/9627
• Subject:
  Minimax inequality;
  multiplicity;
  35J20;
  35J65
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.037
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other