Submitted Paper

Inserted: 12 apr 2023
Last Updated: 12 apr 2023

Year: 2022

Abstract:

We establish a priori $L^\infty$-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<s≤12 the analysis started in 7.

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• EF-2022-11-07.pdf