Limits of solutions to a nonlinear second-order ODE
type: Item
instance of: scholarly article
title: Limits of solutions to a nonlinear second-order ODE
zbMATH Open document ID: 1255.34046
author: Cristian Vladimirescu
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2012-07-16T00:00:00Z
reviewed by: Gheorghe Tigan
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34A40
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6057296
zbMATH Keywords: second-order ODE
zbMATH Keywords: Lyapunov function
zbMATH Keywords: homoclinic solution
MaRDI profile type: Publication
full work available at URL: j.na.2012.04.029
OpenAlex ID: W2052868231
cites work: Q4801761
cites work: Limits of solutions of a perturbed linear differential equation
cites work: Q4824307
cites work: Asymptotic stability of second order ordinary, functional, and partial differential equations
cites work: Q5619320
cites work: Q3215593
cites work: Q3946471
cites work: Integral conditions on the asymptotic stability for the damped linear oscillator with small damping
cites work: Q5569338
cites work: Stability for a Nonlinear Second Order ODE
cites work: Stability for a damped nonlinear oscillator
cites work: Precise damping conditions for global asymptotic stability for nonlinear second order systems
cites work: Precise damping conditions for global asymptotic stability for nonlinear second order systems. II
cites work: Asymptotic Stability for Intermittently Controlled Nonlinear Oscillators
cites work: Existence problems for homoclinic solutions
cites work: Homoclinic solutions for linear and linearizable ordinary differential equations
cites work: Q5308871
cites work: An existence result for homoclinic solutions to a nonlinear second-order ODE through differential inequalities
cites work: Q5608953
DOI: 10.1016/J.NA.2012.04.029
review text: The paper deals with the differential equation NEWLINE\[NEWLINE\ddot{x}+2f(t)\dot{x}+\beta(t)x+g(t,x)=0.NEWLINE\]NEWLINE Based on the method of Lyapunov functions and employing some differential inequalities, the existence of homoclinic orbits is proven.
description: scientific article; zbMATH DE number 6057296