Existence And Multiplicity Of Bound States And Multi-bump Solutions For Two Classes Of Schr?dinger Equations

In recent years,it has been paid more and more attention in the study of Schrodinger equation.This thesis studies mainly the existence and multiplicity of bound states or multi-bump solutions for two classes of Schrodinger equation.The main results are summarized as follows:Chapter 1 gives a brief overview of the research background,the current state of research,the formulation of the problem,and the preliminary knowledge.In Chapter 2,we mainly deal with a class of the p-Laplacian Kirchhoff-Schrodinger equation with potentials vanishing or unbounded at infinity.We prove the existence and concentration behavior of positive solutions for the problem by the variational methods and concentration-compactness principle.In Chapter 3,we consider a class of the quasilinear Choquard equation.By using a change of variables and constructing an auxiliary function,we cloud transform the quasilinear equations into a semilinear one.we show the existence and multiplicity of multi-bump solutions for the problem by the mountain pass geometry and deformation lemma.