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arXiv · 1703.08028

Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well

Lun Guo·Tingxi Hu
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Abstract

In this paper, we are concerned with the existence and asymptotic behavior of least energy solutions for following nonlinear Choquard equation driven by fractional Laplacian $$(-Δ)^{s} u+λV(x)u=(I_α\ast F(u))f(u) \ \ in \ \ R^{N},$$ where $N> 2s$, $ (N-4s)^{+}<α< N$, $λ$ is a positive parameter and the nonnegative potential function $V(x)$ is continuous. By variational methods, we prove the existence of least energy solution which localize near the potential well $int (V^{-1}(0))$ as $λ$ large enough.

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Lun Guo, Tingxi Hu. 2017-04-05. Existence and asymptotic behavior of the least energy solutions for fractional Choquard equations with potential well. https://doi.org/10.1002/mma.4653

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