Existence and non-existence results for a semilinear fractional Neumann problem

2022/11/15 by Cinti, Eleonora, Colasuonno, Francesca
#35A01 #35B09 #35B45 #60G22 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.08315

Abstract

We establish a priori L^∞-estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion coefficient and on the nonlinearity. Moreover, we prove an existence result for radial, radially non-decreasing solutions in the case of a possible supercritical nonlinearity, extending to the case 0

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