Existence Of Solutions For A Class Of Kirchhoff Problem And A Class Of Hamiltonian System

The variational method is a branch of mathematics to study the functional extremum. It dates back to the brachistochrone curve John Bernoulli. The classical variational theory turns the differential equation solving problems to a minimax problems of corresponding functional, having become a basic method in the study of boundary value problems of differential equations. In twentieth century, there are new development, such as the mountain pass theorem, Fountain theorem, linking theorem.This thesis will achieve the solve of a class of Kirchhoff type problems and a class of the second order Hamiltonian systems through the variational method. This thesis is divided into three sections according to contents.Chapter 1 Preference, We introduce some fundamental knowledge and source of the-ory.Chapter 2 We prove the existence solution for a class of Kirchhoff type problems in a bounded domain Ω(?)R3 exist a stationary solution of sign changing.Chapter 3 For a class of the second order Hamiltonian systems by using the local linking lemma and deformation lemma, we will obtain at least two nontrivial homoclinic orbits, where V(t,u) is superquadratic.