A concave-convex elliptic problem involving the fractional Laplacian

2010/06/23 by Brändle, Cristina, Colorado, Eduardo, de Pablo, Arturo · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1006.4510

Abstract

We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize completely the range of parameters for which solutions of the problem exist and prove a multiplicity result.

Cited by

• Fractional critical systems with mixed boundary conditions
• Nonlocal critical problems with mixed boundary conditions and nearly resonant perturbations
• Existence, Nonexistence, and Symmetry of Positive Solutions for Fractional Laplacian Problems

Related

• A critical fractional equation with concave-convex power nonlinearities
• Existence and Multiplicity of Solutions for Fractional p-Laplacian Equation Involving Critical Concave-convex Nonlinearities
• A concave-convex problem with a variable operator
• Concave-convex nonlinearities for some nonlinear fractional equations\n involving the Bessel operator
• A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional p(⋅)-Laplacian