Asymptotic behaviour of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function
type: Item
instance of: scholarly article
title: Asymptotic behaviour of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function
zbMATH Open document ID: 0930.34059
DOI: 10.1016/S0377-0427(98)00024-7
author: N. Markova
author: Drumi Bainov
author: P. S. Simeonov
published in: Journal of Computational and Applied Mathematics
publication date: 2000-01-31T00:00:00Z
review text: The authors consider the nonlinear second-order delay differential equation of the form \[ (r(t)x'(t))'+ f(t,x(t),x(\Delta (t,x(t))))=0. \tag{1} \] Under certain assumptions on the functions \(r,\;f,\;\Delta\) they establish a classification of nonoscillatory solutions to (1) and present conditions for equation (1) to have a nonoscillatory solution of some type. Moreover, in the case when \(f\) is a strongly sublinear (superlinear) function conditions for the oscillation of each regular solution to (1) are stated.
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K11
zbMATH DE Number: 1326340
zbMATH Keywords: second-order nonlinear differential equation with delay
zbMATH Keywords: asymptotic behaviour of solutions
reviewed by: Jan Ohriska
MaRDI profile type: Publication
cites work: Q3969236
cites work: On Oscillation of Solutions of Forced Functional Differential Equations of Second Order
cites work: Q3759218
cites work: Q5806127
cites work: Q5624056
full work available at URL: s0377-0427(98)00024-7
OpenAlex ID: W2028621363
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description: scientific article; zbMATH DE number 1326340