Calculus of Variations and Geometric Measure Theory
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E. Cinti - F. Colasuonno

A nonlocal supercritical Neumann problem

created by cinti on 05 Apr 2019



Inserted: 5 apr 2019

Year: 2019

ArXiv: 1904.02635 PDF


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.

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