Asymptotic decay of solutions of a nonlinear second-order differential equation with deviating argument
type: Item
instance of: scholarly article
title: Asymptotic decay of solutions of a nonlinear second-order differential equation with deviating argument
zbMATH Open document ID: 0674.34079
DOI: 10.1016/0022-247X(89)90297-7
author: M. Cecchi
author: Mauro Marini
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: The purpose of this paper concerns the study of the existence and the asymptotic behaviour of decreasing solutions of second order nonlinear functional differential equations. So results already known for ordinary differential equations, such as the Thomas-Fermi one, the Schrödinger- Persico one, or the ones arising in the law of angular momentum conservation with a time dependent field strength, are generalized in presence of a deviating argument. A section is devoted to sufficient conditions in order that the considered equation has: (i) positive decreasing (negative increasing) solutions, (ii) solutions approaching a nonzero limit as the time t tends towards infinity. This is obtained using techniques which involve a comparison with a suitable linear ordinary differential equation. Another section studies the existence of solutions approaching zero as \(t\to \infty\), via a topological approach. The proof of Theorem 3 gives an estimate of the rate of convergence to zero.
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34E99
zbMATH DE Number: 4103542
zbMATH Keywords: Thomas-Fermi differential equation
zbMATH Keywords: Schrödinger-Persico differential equation
zbMATH Keywords: second order nonlinear functional differential equations
Wikidata QID: Q115364509
reviewed by: Christian Mira
MaRDI profile type: Publication
cites work: On continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals
cites work: Q3903322
cites work: Estimates regarding the decay of solutions of functional differential equations
cites work: Linear Differential and Difference Equations with Monotone Solutions
cites work: On nonoscillatory solutions of functional differential equations with a general deviating argument
cites work: Continuability and estimates of solutions of (a(t)ψ(x)x')' + c(t)f(x) = 0
cites work: Asymptotic behavior of non-linear differential equations via non-standard analysis. Part III. Boundedness and monotone behavior of the equation (a(t)φ(x)x')' + c(t)f(x) = q(t)
cites work: Q3704250
cites work: Oscillatory and asymptotic behavior of sublinear retarded differential equations
cites work: Positive solutions of functional differential equations with singular nonlinear terms
cites work: OSCILLATIONS OF HIGHER-ORDER RETARDED DIFFERENTIAL EQUATIONS GENERATED BY THE RETARDED ARGUMENT
cites work: Q3312543
cites work: Positive bounded solutions for a class of linear delay differential equations
cites work: Some Properties of Solutions of $(r(t)\psi (x)x')' + a(t)f(x) = 0$
cites work: On the asymptotic behavior of the solutions of second order linear differential equations
cites work: Monotone solutions of a class of second order nonlinear differential equations
cites work: Q3693866
cites work: Nonoscillatory solutions of linear differential equations with deviating arguments
cites work: On the existence of nonoscillatory solutions tending to zero at infinity for differential equations with positive delays
cites work: A basic asymptotic criterion for differential equations with deviating arguments and its applications to the nonoscillation of linear ordinary equations
cites work: Strongly Monotone Solutions of Retarded Differential Equations
cites work: Asymptotic nonoscillation under large amplitudes of oscillating coefficients in second order functional equations
cites work: Q5182001
full work available at URL: 0022-247x(89)90297-7
OpenAlex ID: W1993322922
description: scientific article; zbMATH DE number 4103542