Existence Of Normalized Solutions For A L~2-supercritical Nonlinear Fractional Schr(?)dinger Equation

We are concerned with the following nonlinear fractional Schr（?）dinger equation:（-△）^su+V（x）u+ωu=|u|^p-2u,x∈R^N,（P）where s∈（0,1）,N>2s,p∈（2+（4s）/N,（2N）/（N-2s））andωis a parameter.Under certain assumptions on the potential V（x）:R^N→R,we prove that there exists at least one L²-normalized solution（u,ω）∈H^s（R^N）×R⁺of equation（P）.In order to overcome the lack of compactness,the proof is based on a new min-max argument and concentration-compactness methods.The paper is composed of the following chapters:In chapter 1,we introduce the research background and main results.In chapter 2,we give some preliminary knowledge and main lemmas.In chapters 3 and 4,we prove the existence of normalized solutions to（P）under potential V（x）is L^∞bounded or has singularity points respectively by linking theorem.