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The Existence and Multiplicity of Periodic Solutions for Asymptomatically Linear Discrete Systems

Author: TanFengHua
Tutor: GuoZhiMing
School: Guangzhou University
Course: Applied Mathematics
Keywords: Differential equation Discrete Hamiltonian Systems Periodic solution Linking theorem Critical point Index theory Morse theory
CLC: O175.1
Type: Master's thesis
Year: 2010
Downloads: 10
Quote: 0
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Abstract


In this paper, application of critical point theory , Existence and multiplicity of periodic solution of a class of second-order differential equation and a first-order discrete Hamiltonian systems asymptotically linear conditions periodic solution of the second - order differential equations and discrete Hamiltonian system existence problem into a critical point of the corresponding functional existence discuss the first chapter introduces the sources of difference equations and discrete Hamiltonian systems , historical background and some of the results presented , and in order to prove the conclusion convenience necessary prior knowledge of the second chapter focuses on the existence of periodic solutions of autonomous systems , the author first critical point theory and Zp index theory, the periodic solution of the second - order differential equation converted to the critical point of the corresponding functional , then studied asymptotically linear second-order differential equation at infinity and zero at the meet , and the resonance of the infinity of existence of periodic solutions . discussed in Chapter Existence and multiplicity of periodic solution of non - autonomous system , multiple Periodic Solutions of non - Self - Governing system asymptotically linear conditions by the method of combining critical point theory and relative Morse index theory existence theorem of Chapter IV critical point theory and Morse theory to discuss a first-order discrete Hamiltonian periodic solution of the system infinity resonance Existence and multiplicity .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Ordinary Differential Equations
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