A Study Of Multiple Positive Solutions For Schr:odinger-Poisson Systems With Singular And Critical Growth

In this paper,we study the existence of multiple positive solutions for a class of Schr?dinger-Poisson system with singularity and critical growth by means of variational method,critical point theory for nonsmooth functional and the Nehari method,etc.On the one hand,we consider the following logarithmic Schr?dinger-Poisson system with singular term#12 where ??R3 is a smooth bounded domain with boundary ??,00 is a real parameter.By using the critical point theory for nonsmooth functional and variational method,the existence and multiplicity of positive solutions of the system(0.1)are established.On the other hand,we study the solvability of the following Schr?dinger-Poisson system with critical growth#12 where ??R3 is a smooth bounded domain with boundary ??,00,f? L6/(5+?)(?)is a positive function.By using variational method and Nehari manifold method,we obtain that the system(0.2)has the existence of multiple positive solutions.