Normalized bound state solutions of fractional Schrödinger equations with general potential

Abstract

ABSTRACT In this article, we study a class of fractional Schrödinger equation (1) { ( − Δ ) s u = λu + a ( x ) | u | p − 2 u , ∫ R N | u | 2 d x = c 2 , u ∈ H s ( R N ) , where N>2s, s ∈ ( 0 , 1 ) and 0 $ ]]> p ∈ ( 2 , 2 + 4 s / N ) , c > 0 . a ( x ) ∈ C ( R N , 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 (1).