Research On The Existence Of Solutions For Some Kinds Of Planar Schr(?)dinger-Poisson Systems

In this thesis,the existence of solutions for some kinds of planar Schr?dingerPoisson systems is studied by means of variational method.The main contents are as follows:The first chapter introduces the background and the latest research developments of the planar Schrodinger equation.Furthermore,the main research contents and relevant preparatory knowledge of this paper are elaborated.The second chapter studies the following plane Schrodinger-Poisson system:where V ∈ C(R2,[0,∞))is axially symmetric and f∈C(R2×R,R).We consider the subcritical exponential growth of the nonlinear term f(x,u)at infinity,and give it a weaker hypothesis.By the variational method,we obtain the existence of axisymmetric solutions for the planar Schrodinger-Poisson system.When a symmetry condition is added to f(x,u),the existence of multiple solutions of the planar Schrodinger-Poisson system is obtained,and when a monotone condition is added,the existence of variable sign solutions is obtained.The third chapter studies the following plane Schrodinger-Poisson system:where λ≥1,V:R2→R and p>4.We consider the plane Schrodinger-Poisson system with deep well potential and the nonlinear term f is power function,the existence of nontrivial solution is obtained by variational method.The existence of the nontrivial solution of Schrodinger equation is obtained through the deep study of the system solution.The fourth chapter presents the conclusions and outlook in this thesis.