WIAS Preprint No. 2344, (2016)
A nonlocal concave-convex problem with nonlocal mixed boundary data
Authors
- Abdellaoui, Boumediene
- Dieb, Abdelrazek
- Valdinoci, Enrico
ORCID: 0000-0001-6222-2272
2010 Mathematics Subject Classification
- 35R11 35A15
Keywords
- integrodifferential operators, fractional Laplacian, weak solutions, mixed boundary condition, multiplicity of positive solution
DOI
Abstract
The aim of this paper is to study a nonlocal equation with mixed Neumann and Dirichlet external conditions. We prove existence, nonexistence and multiplicity of positive energy solutions and analyze the interaction between the concave-convex nonlinearity and the Dirichlet-Neumann data.
Appeared in
- AIMS Commun. Pure Appl. Anal., 17:3 (2018), pp. 1103--1120.
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