Multiplicity Of Solutions For Sixth Order Asymptotically Linear Equation

In this paper, the existence and multiplicity of solutions for sixth order dif-ferential equations is discussed by index theory.In the first chapter, some basic concepts and results in [7,8] about index theory are given, which are the basic of this paper. Then, at the end of this paper the main results of this paper are exhibited.In the second chapter, we give definition of the index on sixth order linear systems,and then discuss the properties of index. As an application of index the-ory, sixth order asymptotically linear equation is discussed. At the same time an example of the existence of the solution is given. Finally, we give a more general result of the multiplicity of solutions for sixth order equation.