Multiple Existence Of P-laplace Periodic Solutions

This dissertation studies the existence of multiple periodic solutions problems for non-autonomous second order Hamiltonian systems and ordinary p-Laplacian systems by applying the minimax priciple, generalized saddle point theorems etc, We obtian a series of results on the existence of multiple solutions.The obtained results extend and improve some known results in the existing references.This dissertation divided into three chapters.The main contents are as follows:In the first Chapter, we introduce the historical background and the up-to-date progress of problems which will be investigated and preliminary tools and main results of this paper.In Chapter 2,We consider the following non-autonomous second order Hamiltonian system We assume that the nonlinearity satisfies some periodicity,linearity,sub-linearity and other conditions.Under these assumptions, some meaningful results on the existence and multiplicity of periodic solutions are obtained by using minimax priciple,generalized saddle point theorems.In Chapter 3, we consider the more general ordinary p-Laplace system We will extend the second order non-autonomous systems to the more general ordinary p-Laplace systems, The results obtained enrich the ones in chapter 2.