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arXiv · 2608.11842

Existence and non-existence results for a fractional Lane-Emden equation with nonlocal Neumann conditions

Eleonora Cinti·Matteo Talluri·Tobias Weth
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Abstract

We consider the fractional Lane-Emden equation with a nonlocal Neumann condition in a half-space. We establish the existence of non-constant solutions for the critical problem in any dimension. On the other hand, we show that, in dimension $n=1$, the subcritical problem admits only the trivial solution. This result follows from a new Pohozaev-type identity, which we obtain by using suitable decay estimates for the solutions.

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Eleonora Cinti, Matteo Talluri, Tobias Weth. 2026-08-12. Existence and non-existence results for a fractional Lane-Emden equation with nonlocal Neumann conditions. https://arxiv.org/abs/2608.11842

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