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Types of Second Order Functional Differential Equations and asymptotic behavior

Author: DaiYi
Tutor: ZhangMengQiu
School: Central South University
Course: Applied Mathematics
Keywords: Oscillation Asymptotic behavior Nonlinear Neutral Time Delay
CLC: O175
Type: Master's thesis
Year: 2006
Downloads: 32
Quote: 0
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Abstract


This paper studies the Second Order Functional Differential Equations and asymptotic behavior of the text consists of four chapters . Chapter I gives an overview of functional differential equations background and development of the status quo . Chapter II Young inequality of equation (a (t) ((x (t) p (t) x (t-τ)) ') σ )' q (t) | x (t-σ 1 ) | α sgn x (t-σ 1 ) r (t) | x (t-σ 2 ) | β sgn x (t-σ 2 ) = 0. Vibration , existing results as a special case of this article , the promotion of the existing conclusion . Chapter III study using direct analysis method for a class of second order nonlinear functional differential equation ( a ( t) (x '( t ) ) σ ) ' p ( x (t ) ) x '(t) q (t) f (x (g (t))) = 0. Oscillatory and asymptotic behavior of the solution of the equation Oscillatory and asymptotic behavior of a sufficient condition . Chapter H - function method and integral squared skills mainly of second order differential equations (r ( t ) φ ( x ( t) ) z ' ( t )) ' q ( t) g ( x ( t ) , x '(t)) k (t) f (x (σ (t))) = 0, t ≥ t 0 . Z (t) = x (t) p (t) x (τ (t)) vibration , sufficient conditions for oscillation of the equation . Relatively small on findings obtained results generalize the related results in the literature .

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