Mountain Pass solutions for non-local elliptic operators

Raffaella Servadei, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

491 Citations (Scopus)

Abstract

The purpose of this paper is to study the existence of solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a non-trivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. We prove this result for a general integrodifferential operator of fractional type and, as a particular case, we derive an existence theorem for the fractional Laplacian, finding non-trivial solutions of the equation. As far as we know, all these results are new.

Original languageEnglish
Pages (from-to)887-898
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume389
Issue number2
DOIs
Publication statusPublished - 15 May 2012
Externally publishedYes

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