Ground states for a fractional scalar field problem with critical growth

Vincenzo Ambrosio

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arXiv · 1605.06788

Ground states for a fractional scalar field problem with critical growth

Vincenzo Ambrosio

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Abstract

We prove the existence of a ground state solution for the following fractional scalar field equation $(-\Delta)^{s} u= g(u)$ in $\mathbb{R}^{N}$ where $s\in (0,1), N> 2s$,$ (-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}(\mathbb{R}, \mathbb{R})$ is an odd function satisfying the critical growth assumption.

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Vincenzo Ambrosio. 2016-05-22. Ground states for a fractional scalar field problem with critical growth. https://arxiv.org/abs/1605.06788

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