Asymptotic and oscillatory behavior of a class of second order functional differential equations
type: Item
instance of: scholarly article
title: Asymptotic and oscillatory behavior of a class of second order functional differential equations
zbMATH Open document ID: 0726.34055
published in: Rocky Mountain Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Oscillation theorems are proved for functional-differential equations of the type \[ (1)\quad -(r(t)g(x(t))x'(t))'=\quad p(t)x'(t)+q(t)f(x[\phi (t)]),\quad t\geq t_ 0 \] under suitable conditions on the functions f,g,p,q,r,\(\phi\). In particular, q(t) is allowed to change sign in \([t_ 0,\infty)\) and \(\phi\) (t) can be of retarded or advanced type. One theorem gives sufficient conditions for every solution x(t) of (1) to be either oscillatory at \(\infty\) or to decay monotonely to zero as \(t\to \infty\).
reviewed by: Charles A. Swanson
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 4198520
zbMATH Keywords: Oscillation theorems
zbMATH Keywords: functional-differential equations
zbMATH Keywords: advanced type
zbMATH Keywords: decay
author: Bikkar S. Lalli
author: Said R. Grace
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181073063
OpenAlex ID: W1979417286
cites work: Some oscillation theorems for second order differential equations
cites work: Oscillation criteria for non-linear second order equations
cites work: Q4100806
cites work: Oscillation theorems for certain second order perturbed nonlinear differential equations
cites work: Asymptotic and oscillatory behavior of solutions of a class of second order differential equations with deviating arguments
cites work: Oscillations in second order differential equations with alternating coefficients
cites work: Oscillation and convergence to zero of solutions of damped second-order nonlinear differential equations
cites work: Oscillation Theorems for Nonlinear Second Order Differential Equations with a Nonlinear Damping Term
cites work: Oscillation theorems for perturbed nonlinear differential equations
cites work: Q4167008
cites work: Q5682643
cites work: Q4134269
cites work: Oscillation and asymptotic behavior of solutions of linear differential inequalities and equations with deviating arguments
cites work: Q5614148
cites work: A Second Order Superlinear Oscillation Criterion
cites work: Integral Averages and Second Order Superlinear Oscillation
cites work: Q4050946
cites work: Classification of second order linear differential equations with respect to oscillation
cites work: Q5575789
cites work: Q4075816
cites work: Oscillation Theorems for Nonlinear Second Order Differential Equations with Damped Term
DOI: 10.1216/RMJM/1181073063
description: scientific article; zbMATH DE number 4198520