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

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 $$(-\Delta {)}^{s}u+\lambda V(x)u=(I_{\alpha }\ast F(u))f(u)in{R}^N,$$ where $N>2s$, $(N-4s{)}^{+}<\alpha <N$, $\lambda$ 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 $\lambda$ large enough.

arXiv comment19 pages, text overlap with arXiv:1703.08028

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Cited by in corpus (2)

• Multiple and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent
• Saddle solutions for the fractional Choquard equation