Infinitely many radial and non-radial solutions for a fractional Schrödinger equation

In this paper, we study the following fractional Schrödinger equation (−Δ)su+V(|x|)u=f(|x|,u),x∈RN, where (−Δ)s(s∈(0,1))(−Δ)s(s∈(0,1)) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions for N≥2N≥2, a sequence of non-radial solutions for N=4N=4 or N≥6N≥6, and a non-radial solution for N=5N=5.