| 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. |
