Ground State Solutions For Kirchhoff-type Equations

In this thesis, by using some basic approaches of variational methods such as minimax method and Nehari manifold, we prove the existence of ground state solutions.In the first chapter, we recall some background and results of the related Kirch-hoff equation. We also discribc the problem we will study.In the second chapter, we consider the following Kirchhoff-type equation with Hartree-type nonlinearities where a>0, b>0 are constants, p?(2,6-?), ??(0,3) and * denotes the convolution of two functions in R3. The function V(x) is periodic in R3, satisfying the following conditions.(A1) V (x)?C(R3, R) and V(x)>0 for all x?R3;(A2) V(x) is 1-periodic with respect to x1,x2, x3. Under various hypotheses, we prove the existence of ground state solutions for e-quation under various hypotheses via the Nehari manifold and the concentration compactness principle.In the third chapter, we replace the right part of (Qi) with a general nonlinear function. We study the following nonlinear Kirchhoff equation and prove the existence of ground state, where f(x, u) satisfies some assumptions.