Giovanni Molica Bisci (Author), Dušan Repovš (Author)

Abstract

This work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. In addition, we require rather general assumptions on the local operator. As far as we know, this result is new and represent a fractional version of a classical theorem obtained working with Laplacian equations.

Keywords

partial differential equations;quasilinear elliptic equations;nonlocal problems;fractional equations;Mountain Pass Theorem;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956
COBISS: 17294425 Link will open in a new window
ISSN: 1120-6330
Views: 561
Downloads: 369
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Other data

Type (COBISS): Article
Pages: str. 161-176
Volume: ǂVol. ǂ26
Issue: ǂiss. ǂ2
Chronology: 2015
DOI: http://dx.doi.org/10.4171/RLM/700
ID: 11233722