Classifications of solutions of second-order nonlinear neutral differential equations of mixed type-Reference-Cited by-同舟云学术

Classifications of solutions of second-order nonlinear neutral differential equations of mixed type

Published:2012-12 Issue:1 Volume:2012 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Thandapani E,Padmavathi S,Pinelas S

Abstract

Abstract In this paper the authors classified all solutions of the second-order nonlinear neutral differential equations of mixed type,

( a ( t ) ( x ( t ) + b x ( t − τ 1 ) + c x ( t + τ 2 ) ) ′ ) ′ + p ( t ) x α ( t − σ 1 ) + q ( t ) x β ( t + σ 2 ) = 0 ,

into four classes and obtained conditions for the existence/non-existence of solutions in these classes. Examples are provided to illustrate the main results. MSC:34C15.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

https://link.springer.com/content/pdf/10.1186/1687-1847-2012-226.pdf

Reference12 articles.

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2. Hale JK: Theory of Functional Differential Equations. Springer, New York; 1977.

3. Thandapani E, Maria Susai Manuel M: Oscillatory and non-oscillatory behaviour of second order neutral delay differential equations. Eng. Simul. 1998, 15: 159–167.

4. Thandapani E, Muthulakshmi V, Grafe JR: Classifications of solutions of second order nonlinear neutral delay differential equations with positive and negative coefficients. Int. J. Pure Appl. Math. 2010, 64: 159–170.

5. Bainov DD, Mishev DP: Oscillation Theory for Neutral Differential Equations with Delay. Hilger, New York; 1991.

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