A supercritical nonlocal Neumann problem involving non-homogeneous fractional Laplacian

2024/06/27 by Temgoua, Remi Yvant
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.19250

Abstract

In this paper, we study the existence of positive non-decreasing radial solutions of a nonlocal non-standard growth problem ruled by the fractional g-Laplace operator with exterior Neumann condition. Our argument exploits some properties of fractional Orlicz-Sobolev spaces combined with a variational principle for nonsmooth functionals, which allows to deal with problems lacking compactness.

Related

• Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces
• Radial positive solutions for mixed local and nonlocal supercritical Neumann problem
• Nonlocal problems with critical Hardy nonlinearity
• Nonlocal problems at critical growth in contractible domains
• Three solutions for a nonlocal problem with critical growth