Fu(?)(?)k Spectrum And Existence Of Solutions For Normal Homogeneous Equations

In this paper we mainly utilize the knowledge of Fucik spectrum under the follow-ing jumping nonlinear conditions.#12With those conditions,we use the variational method to study the existence of solutions for Sturm-Liouville boundary value problems of Duffing Equations,where? ?[0,?),??(0,?].x+f(t,x)=0,x(0)cos ?-x(0)sin ?=0,x(1)cos ?-x(1)sin?=0.There are three chapters in this whole essay.We present the main results in the first chapter.In the second chapter,we mainly discuss the Fucik spectrum for some special value of ? and ?,and give the application of such theorem.We then show the proof of that theorem in the third chapter.