On nonlinear fractional Choquard equation with indefinite potential and general nonlinearity

In this paper, we consider a class of fractional Choquard equations with indefinite potential (-Delta)(alpha) u + V(x)u = [integral(RN) M(epsilon y)G(u)/vertical bar x - y vertical bar(mu) dy]M(epsilon x)g(u), x is an element of R-N, where alpha is an element of (0, 1), N > 2 alpha, 0 < mu < 2 alpha, epsilon is a positive parameter. Here (-Delta)(alpha) stands for the fractional Laplacian, V is a linear potential with periodicity condition, and M is a nonlinear reaction potential with a global condition. We establish the existence and concentration of ground state solutions under general nonlinearity by using variational methods.