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.

19 pages, text overlap with arXiv:1703.08028

References in corpus (4)

• Groundstates of nonlinear Choquard equations: Hardy-Littlewood-Sobolev critical exponent
• Ground state solutions for non-autonomous fractional Choquard equations
• Profile decompositions and Blowup phenomena of mass critical fractional Schrödinger equations
• Uniqueness and Nondegeneracy of Ground States for Choquard Equations in three dimensions

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