Multiplicity and concentration of solutions for fractional Schrödinger equation with sublinear perturbation and steep potential well

Abstract

In this paper, we investigate the following fractional Schrödinger equation with sublinear perturbation and steep potential well {(−△)su+λV(x)u=f(x,u)+α(x)|u|ν−2uinRN,u∈Hs(RN), where 0<s<1,2s<N,λ>0,1<ν<2, f∈C(RN×R) is of subcritical growth. By using variational methods, we prove that such a class of equations possess at least two nontrivial solutions. Moreover, the phenomenon of concentration of solutions is explored as well.