Multi-periodic Solutions For Two Kinds Of Differential Equations

Variational principle is a common principle in the nature, and many problems can come down to the problems of critical points of a special fuctional under some specific conditions. The periodic solutions of differential equations can usually be changed into variational problems to gain the existence and numbers of the solutions to differential equations. Modern variational methods have developed greatly in recent twenty years, which is widely used in many branches of mathematics.By using variational structure and Z2—group index theory, we mainly study the periodic solutions for some second-order Hamiltonian system and some second-order neutral functional differential equation. The whole thesis contains three chapters. In the first chapter, we introduce the historical situation and the present development concerned the problem of periodic solutions for differential equation, critical point theory and some necessary lemmas. In Chapter 2 and chapter 3, by using of varia-tional structure and Z2—group index theory, we discuss the multiple periodic solutions for some second-order Hamiltonian system and some second-order neutral functional differential equation, and we rich and promote the conclusions in original literatures...