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Variational method in the fourth-order and second-order differential boundary value differential System

Author: ZhangGuoDong
Tutor: SunHongRui
School: Lanzhou University
Course: Basic mathematics
Keywords: Fourth-order difference equation Boundary Value Problems Parameter Calculus of variations Critical point theory Differential System Periodic solution
CLC: O175.7
Type: Master's thesis
Year: 2011
Downloads: 21
Quote: 0
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Abstract


This paper considers using the variational method with a class of fourth order difference equation parameters Existence of Solutions of Boundary Value Problems and Periodic Solutions of Second Order Differential Existence and nonexistence in the first chapter introduces the problem background , current status , and the main results and some preliminary knowledge , the second chapter to consider fourth order difference equation existence of multiple solutions , we established the appropriate function space, function space on the basis of this equation to establish the corresponding variational functionals , the existence of this boundary value problem into a functional space in the function of the existence of critical points , reuse mountain theorems , Clark theorem and around the critical point theorem existence theorem a sufficient condition , and finally lifted several examples verify the results obtained . third chapter we discuss the second-order differential system (P2) T-periodic solutions of a non- trivial existence and nonexistence . use Cartesian product we build higher dimensional function space, function space created directly corresponds to a differential system of variational functionals , and then using the critical point theorem gives us the existence of periodic solutions for differential systems and there is no sufficient conditions .

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