Multiple positive solutions for Schrodinger-Poisson system involving singularity and critical exponent

摘要

In this paper, the existence and multiplicity of positive solutions is established for Schrodinger-Poisson system of the form-Delta u+phi u=u5+lambda|x|beta u gamma,in omega,-Delta phi=u2,in omega,u>0,in omega,u=phi=0,on partial differential omega,where 0 is an element of omega is a smooth bounded domain in R3, gamma is an element of(0,1),0 <=beta<5+gamma 2, and lambda > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.