Least Energy Sign-changing Solutions Of Schr(?)dinger-Poisson System With Critical Growth

In this master thesis,we pay an attention to the existence and the asymptot-ic behavior of least energy sign-changing solutions for the following Schr¨odinger-Poisson system with Sobolev critical exponent (?)whereV(x)is a smooth function and μ,λ>0.In chapter one,the background for Schr¨odinger-Poisson system are presented.Then the paper’s framework and main results are also summarized.In chapter two,some notations and preparatory results are stated.In chapter three,based on some existing results for Schr¨odinger-Poisson equa-tions,under suitable conditions onf(u),for μ large sufficiently and all λ>0,by using constraint variational method and the quantitative deformation lemma,we obtain a least energy sign-changing(or nodal)solution u_λ to this problem,and its energy is strictly larger than twice that of the ground state solutions.Moreover,we study the asymptotic behavior of u_λ as the parameter λ↘0.