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arXiv · 2211.08315

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

Eleonora Cinti·Francesca Colasuonno
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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 $0<s\le 1/2$ the analysis started in [7].

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Eleonora Cinti, Francesca Colasuonno. 2022-11-15. Existence and non-existence results for a semilinear fractional Neumann problem. https://arxiv.org/abs/2211.08315

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