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arXiv · 1312.7068

Positive solutions to some nonlinear fractional Schr\"odinger equations via a min-max procedure

Gilles Evéquoz·Mouhamed Moustapha Fall
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Abstract

The existence of a positive solution to the following fractional semilinear equation is proven, in a situation where a ground state solution may not exist. More precisely, we consider for $0 0$, $Q\geq 0$ are bounded functions converging to $1$ as $|x|\to\infty$. Using a min-max procedure introduced by Bahri and Li we prove the existence of a positive solution under one-sided asymptotic bounds for $V$ and $Q$.

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Gilles Evéquoz, Mouhamed Moustapha Fall. 2013-12-26. Positive solutions to some nonlinear fractional Schr\"odinger equations via a min-max procedure. https://arxiv.org/abs/1312.7068

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