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Asymptotic Properties of Several Classes of Nonlinear Differential Equations
Author: WuXiLang
Tutor: YangJianFu；DingHuiSheng
School: Jiangxi Normal University
Course: Applied Mathematics
Keywords: Duffing equations Shunting inhibitory cellular neural networks Liénard equations Dynamical systems Delay Existence Exponential convergence behavior Almost periodic solutions Uniqueness Anti periodic solutions
CLC: O175.12
Type: Master's thesis
Year: 2010
Downloads: 22
Quote: 0
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Abstract
In this thesis, we study some important asymptotic properties of several classes of nonlinear differential equations. It consists of four chapters.In chapter 1, the background and history of problems which we discuss in this thesis are briefly addressed. Besides, some definitions and basic results are given in this chapter.In chapter2, we discuss the following nonlinear Duffing equation with a deviating argument:We give some new sufficient conditions for the existence and uniqueness of almost periodic solutions of the above Duffing equation. In addition, in the case ofIn chapter 3, we investigate the following general dynamical systems :which unify some extensively studied shunting inhibitory cellular neural networks with delays. Under some suitable conditions, a new theorem is established to ensure that all the solutions of the dynamical systems converge exponentially to the zero point, which substantially extend and improve some important results in the literature.In chapter 4, we consider the following Liénardtype equation:Sufficient conditions for the existence and uniqueness of antiperiodic solutions of the equation are established .

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