A nonlocal concave-convex problem with nonlocal mixed boundary data
- Abdellaoui, Boumediene
- Dieb, Abdelrazek
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 35A15
- integrodifferential operators, fractional Laplacian, weak solutions, mixed boundary condition, multiplicity of positive solution
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.
- AIMS Commun. Pure Appl. Anal., 17:3 (2018), pp. 1103--1120.