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arXiv · 1601.06284

Ground states for superlinear fractional Schr\"odinger equations in \R^{N}

Vincenzo Ambrosio
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Abstract

In this paper we study ground states of the following fractional Schr\"odinger equation (- \Delta)^{s} u + V(x) u = f(x, u) \, \mbox{ in } \, \R^{N}, u\in \H^{s}(\R^{N}) where $s\in (0,1)$, $N>2s$ and $f$ is a continuous function satisfying a suitable growth assumption weaker than the Ambrosetti-Rabinowitz condition. We consider the cases when the potential $V(x)$ is $1$-periodic or has a bounded potential well.

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Vincenzo Ambrosio. 2016-01-23. Ground states for superlinear fractional Schr\"odinger equations in \R^{N}. https://arxiv.org/abs/1601.06284

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