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

10.20347/WIAS.PREPRINT.2344

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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