A nonlocal concave-convex problem with nonlocal mixed boundary data
Boumediene Abdellaoui, Abdelrazek Dieb, Enrico Valdinoci
TL;DR
This paper investigates a nonlocal boundary value problem with mixed exterior conditions, analyzing the existence, nonexistence, and multiplicity of positive solutions and how the nonlinearities interact with boundary data.
Contribution
It introduces new results on the solution structure of nonlocal problems with mixed boundary conditions, highlighting the effects of concave-convex nonlinearities.
Findings
Proves existence of positive solutions under certain conditions.
Establishes nonexistence results for specific parameter ranges.
Identifies multiple solutions depending on the nonlinear interaction.
Abstract
The aim of this paper is to study a nonlocal problem with a mixed Dirichlet-Neumann exterior condition. We prove existence, nonexistence and multiplicity of positive energy solutions and describe the interaction between the concave-convex nonlinearity and the Dirichlet-Neumann data.
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