Existence and concentration of ground state solutions for a class of fractional Schrödinger equations

Article type: Research Article

Authors: Chen, Zhuo | Ji, Chao^{; *}

Affiliations: Department of Mathematics, East China University of Science and Technology, 200237 Shanghai, China

Correspondence: [*] Corresponding author. E-mail: jichao@ecust.edu.cn.

Abstract: In this paper, by using variational methods, we study the existence and concentration of ground state solutions for the following fractional Schrödinger equation (−Δ)αu+V(x)u=A(ϵx)f(u),x∈RN, where α∈(0,1), ϵ is a positive parameter, N>2α, (−Δ)α stands for the fractional Laplacian, f is a continuous function with subcritical growth, V∈C(RN,R) is a ZN-periodic function and A∈C(RN,R) satisfies some appropriate assumptions.

Keywords: Concentration of solutions, ground state, fractional Schrödinger equations, periodic potential, Nehari manifold

DOI: 10.3233/ASY-211680

Journal: Asymptotic Analysis, vol. 126, no. 3-4, pp. 229-253, 2022