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The Existence of Homoclinic Orbit for a Class of Second-order Singular Differential Equation

Author: SuHeng
Tutor: GuoZhiMing
School: Guangzhou University
Course: Applied Mathematics
Keywords: Second Order Singular Boundary Value Problems Single Mediation Homoclinic orbit Critical point theory Shooting method
CLC: O175.8
Type: Master's thesis
Year: 2011
Downloads: 23
Quote: 0
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Abstract


This paper mainly positive axis [0, ∞) as a class discussion on the Second Order Singular Boundary Value Problems : (p (t) u ')' = c (t) p (t) f (u), u ' (0) = 0, u (∞) = 0, where p (0) = 0. singularity of such research background , on the one hand from the ball or RN to find elliptic equation u = f (u) in diameter to the solution of research, on the other hand due to non- homogeneous fluid micro- bubble formation. studied boundary value problem in [0, ∞) strictly monotonically decreasing positive solutions that homoclinic solutions by using critical point theory and combining shooting method to analyze certain singular differential properties of solutions , homoclinic solution obtained sufficient conditions for existence of a series , to a certain extent, has been extended and improved results in Chapter 2 , the application of critical point theory for a class positive Solutions of singular Boundary Value Problems monotonically decreasing existence , first in a new definition of the Hilbert space and Singular Boundary Value established on the corresponding variational framework , and its nature and that some important inequalities are discussed ; and the use of tiny singular Boundary Value Problems of principle has been the existence of positive solutions ; through making positive solutions obtained variational functionals minimum value of this nature , and further analysis of the monotone decreasing existence of Positive Solutions for Chapter 3 of Banach contraction mapping principles study of initial value problem for a class of singular existence of positive solutions , and discusses the nature of the solution . application Chapter 2.3 the results obtained in Chapter 4, combined with the shooting method at f respectively satisfy boundedness and sub- linear growth conditions of the case has been singular differential series homoclinic solutions exist guidelines.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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