Research On The Existence Of Solutions For Schr?dinger-Poisson Systems And Quasilinear Elliptic Equation

In the thesis,we used the variational methods and the critical point theory,we study two classes of Schrodinger-Poisson systems and a class of quasilinear Schrodinger equation,the dissertation consists of five chapters.The main contents are as follows:In Chapter 1,we briefly introduce the research background,and give some necessary preliminary tools:definition,theorems,notations.In Chapter 2,we study the Schrodinger-Poisson system with indefinite nonlinearity#12 where ?,?>0,2<p<4.k(x)is a positive function in R3,a(x)? C(R3)and a(x)changes sign.The system has at least one positive solution when ? within the appropriate range.In Chapter 3,we consider the existence of solution for the following asymptotically linear quasilinear Schrodinger equation-?u+V(x)u-k?[(1+u2)1/2]u/(2(1+u2)1/2=f(u),in RN,where N? 3,k>0 is a parameter and V,f satisfy some appropriate assumptions.In Chapter 4,we investigate the Schrodinger-Poisson system involving negative nonlocal term and critical exponent on whole space.(?)in R3,in R3,where l(x)satisfies some mild assumptions,Then system has at least one positive ground state solution.In Chapter 5,we consider the existence of nontrivial solutions for the following Schrodinger-Poisson system(?)in ?,in ?,on ??,where b is a parameter and ??R3 is a smooth bounded domain,f?C(? ×R,R)satisfies some sublinear and superlinear assumptions,Then system has at least one nontrivial solution.