Open Access
2014 On Asymptotic Behavior of Solutions of Generalized Emden-Fowler Differential Equations with Delay Argument
Alexander Domoshnitsky, Roman Koplatadze
Abstr. Appl. Anal. 2014(SI27): 1-13 (2014). DOI: 10.1155/2014/168425

Abstract

The following differential equation u ( n ) ( t ) + p ( t ) | u ( t ) ) | μ ( t )  sign u ( σ( t ) ) = 0 is considered. Here p L loc ( R + ; R + ) , μ C ( R + ; ( 0 , + ) ) , σ C ( R + ; R + ) , σ ( t ) t , and lim t + σ( t ) = + . We say that the equation is almost linear if the condition lim t + μ ( t ) = 1 is fulfilled, while if lim sup t + μ ( t ) 1 or lim inf t + μ ( t ) 1 , then the equation is an essentially nonlinear differential equation. In the case of almost linear and essentially nonlinear differential equations with advanced argument, oscillatory properties have been extensively studied, but there are no results on delay equations of this sort. In this paper, new sufficient conditions implying Property A for delay Emden-Fowler equations are obtained.

Citation

Download Citation

Alexander Domoshnitsky. Roman Koplatadze. "On Asymptotic Behavior of Solutions of Generalized Emden-Fowler Differential Equations with Delay Argument." Abstr. Appl. Anal. 2014 (SI27) 1 - 13, 2014. https://doi.org/10.1155/2014/168425

Information

Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07021850
MathSciNet: MR3166572
Digital Object Identifier: 10.1155/2014/168425

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI27 • 2014
Back to Top