Solvability And Multiplicity Of Solutions For A Kind Of Forth Order Differential Equations

In this paper, we discuss the existence and multiplicity of a fourth-order nonlinear differen-tial equation u(4)(t)-pu(t)-g(t, u(t))=e(t),t∈[0, T], u(0)=u(T)=w(0)=u(T)=0, where P>-(2π/T)2In the introduction, we introduce the related background and development of variational methods, illustrate the content, backgroud and recent development of the problem we will study.In Chapter1, we present some definitions and theorems we will need.In Chapter2, we study the existence and multiplicity of a class of fourth-order equation. By some critical point theorems, we obtain the existence and multiplicity of a kind of fourth-order equations.