Non-oscillating solutions of a generalized system of ODEs with derivative terms
type: Item
instance of: scholarly article
title: Non-oscillating solutions of a generalized system of ODEs with derivative terms
zbMATH Open document ID: 1495.34055
author: B. V. K. Bharadwaj
author: Pallav Kumar Baruah
published in: Nonautonomous Dynamical Systems
publication date: 2022-01-11T00:00:00Z
review text: A system of ordinary differential equations \[ x_1^{(n_1)}(t)+h_1(t,x_1,x_1',\dots,x_1^{(N_1)},x_2,x_2',\dots,x_2^{(N_2)})=0, \] \[ x_2^{(n_2)}(t)+h_2(t,x_1,x_1',\dots,x_1^{(N_1)},x_2,x_2',\dots,x_2^{(N_2)})=0, \] where \(h_1\), \(h_2\) are real valued continuous functions on \([t_0,\infty)\times \mathbb{R}^{N_1+N_2}\), \(t\geq t_0>0\), and \(n_i>1\) are integers with \(0 \leq N_i\leq n_i-1\), \(i=1,2\), is considered. The existence of a solution which does not oscillate is proved. The fixed point technique is applied to show that under certain conditions there exists at least one solution to the system which is not only non-oscillating, but also asymptotically constant.
reviewed by: Josef Diblík
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7455150
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: fixed-point theorem
zbMATH Keywords: non-oscillation
MaRDI profile type: Publication
full work available at URL: msds-2020-0136
OpenAlex ID: W4205935804
cites work: Existence of positive radial solutions for elliptic systems
cites work: Asymptotic to polynomials solutions for nonlinear differential equations
cites work: Q4816657
cites work: On the oscillatory behaviour of a second order nonlinear differential equation
cites work: Positive solutions of second-order differential equations
cites work: Q3025607
cites work: Q5187747
cites work: Positive solutions of a system of coupled second order equations with three point boundary conditions
cites work: Positive solutions for systems of nth order three-point nonlocal boundary value problems
DOI: 10.1515/MSDS-2020-0136
description: scientific article; zbMATH DE number 7455150