The Solvability Study Of A Class Of Fractioanl Schr(?)dinger Equation

In recent years,the fractional Schr（?）dinger-Poisson equation,which has e-volved from quantum mechanical electromagnetic field model,Hartee-Fock model or semiconductor theory,has become more and more popular among scholars.The e-quation is used to describe the motion state of particles in space and time in fractional quantum mechanics.In this the paper,we investigate the existence and multiplicity of solutions for a class of fractional Schr（?）dinger-Poisson equation with critical nonlin-earity and singular term via variational method and Nehari manifold（?）where s∈（3/4,1）,γ∈（0,1）,λ>0 is a real parameter,2_s^*=6/3-2s is the fractional critical Sobolev exponent.The operator（-Δ）s is the fractional Laplacian,which can be defined by the usual Fourier transform（-Δ）su =F-1（|ξ|2s Fu）（ξ∈R³）.f∈L^∞（R³）∩ L2_s^*/2s^*-1+γ（R³）is a nonnegative function.Firstly,the physical background of the research question,the current research s-tatus at home and abroad,and some preliminary tools used in the proof of main results are given.Then,we decompose the Nehari manifold N_λ which is defined by energy functional associated to the equation（A）into two intersecting submanifolds N_λ^±.Finally,we establish two positive solutions in the two submanifolds,respectively,and one of the solutions to N_λ⁺ is a positive ground state solution.