Description

• Title:
  Saddle point solutions for non-local elliptic operators
• Creator:
  Fiscella, Alessio
• Description:
  The paper deals with equations driven by a non-local integrodifferential operator $\mathcal L_K$ with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a solution for them using the Saddle Point Theorem. We prove this result for a general integrodifferential operator of fractional type and from this, as a particular case, one can derive an existence theorem for the fractional Laplacian, finding solutions of the equation $$ \begin{cases} (-\Delta)^s u=f(x,u) & {\mbox{in }} \Omega,\\ u=0 & {\mbox{in }} \mathbb{R}^n\setminus \Omega, \end{cases} $$ where the nonlinear term $f$ satisfies a linear growth condition.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.04.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 44, No 2 (December 2014); 527 - 538;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.059/8176
• Subject:
  Integrodifferential operators;
  fractional Laplacian;
  variational techniques;
  Saddle Point Theorem;
  Palais-Smale condition;
  Primary 49J35;
  35A15;
  35S15;
  Secondary 47G20;
  45G05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.059
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other