Normalized bound state solutions of fractional Schrödinger equations with general potential

In this article, we study a class of fractional Schrödinger equation (1) {(−Δ)su=λu+a(x)|u|p−2u,∫RN|u|2dx=c2,u∈Hs(RN),(1) where N>2s, s∈(0,1) and p∈(2,2+4s/N),c>0. a(x)∈C(RN,R) is a positive potential function. By using fixed-point theorem of Brouwer, barycenter function and variational method, we obtain the existence of normalized bound solutions for problem (Equation1(1) {(−Δ)su=λu+a(x)|u|p−2u,∫RN|u|2dx=c2,u∈Hs(RN),(1) ).