A nonlocal supercritical Neumann problem

Abstract

We establish existence of positive non-decreasing radial solutions for a nonlocal nonlinear Neumann problem both in the ball and in the annulus. The nonlinearity that we consider is rather general, allowing for supercritical growth (in the sense of Sobolev embedding). The consequent lack of compactness can be overcome, by working in the cone of non-negative and non-decreasing radial functions. Within this cone, we establish some a priori estimates which allow, via a truncation argument, to use variational methods for proving existence of solutions. As a side result, we prove a strong maximum principle for nonlocal Neumann problems, which is of independent interest.

32 pages, 0 figures. In version v2, two typos in Lemma 3.6 have been fixed, with respect to the published version

References in corpus (6)

• Increasing radial solutions for Neumann problems without growth restrictions
• Strong maximum principles for fractional Laplacians
• A p-Laplacian supercritical Neumann problem
• On the Interplay of Regularity and Decay in Case of Radial Functions I. Inhomogeneous spaces
• Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions
• A $p$-Laplacian Neumann problem with a possibly supercritical nonlinearity

Cited by in corpus (1)

• A general framework for nonlocal Neumann problems