Oscillations of second order nonlinear ODEs with impulses
type: Item
instance of: scholarly article
title: Oscillations of second order nonlinear ODEs with impulses
zbMATH Open document ID: 0877.34014
author: Yongshao Chen
author: Weizhen Feng
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-11-26T00:00:00Z
review text: Four oscillation theorems and six corollaries are proved for the semilinear impulse problem \[ \begin{cases} -y''= f(t,y)\quad\text{in }I= [t_0,\infty),\;t\neq t_k,\;k=1,2,\dots\\ y(t^+_0)= y_0,\;y'(t^+_0)= y_0'\\ y(t^+_k)= g_k(y(t_k)),\;q'(t^+_k)= h_k(y'(t_k)),\;k=1,2,\dots\end{cases}\tag{1} \] for \(f\in C(I\times\mathbb{R},\mathbb{R})\), \(sf(t,s)>0\) for all \(s\neq 0\), \(g_k, h_k\in C(\mathbb{R},\mathbb{R})\), \(g_k(s)/s\), \(h_k(s)/s\) are bounded above and below by positive constants for all \(s\neq 0\), and \(0\leq t_0<t_1<\cdots< t_k\to+\infty\) as \(k\to\infty\). The results provide various sufficient conditions for all solutions \(y\) of (1) to be oscillatory at \(\infty\). Examples are included for linear, superlinear, and sublinear differential equations, indicating that insertion of impulses can transform nonoscillatory problems into oscillatory ones.
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1031640
zbMATH Keywords: semilinear impulse problem
zbMATH Keywords: oscillatory
zbMATH Keywords: linear differential equations
zbMATH Keywords: sublinear differential equations
zbMATH Keywords: insertion of impulses
zbMATH Keywords: nonoscillatory
reviewed by: Charles A. Swanson
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5378
OpenAlex ID: W2035367433
cites work: Q3995625
cites work: On second-order non-linear oscillations
cites work: Q3843831
cites work: Oscillation of solutions to second-order nonlinear differential equations
cites work: A Note on Second Order Nonlinear Oscillation
cites work: Q5620001
cites work: Q5647263
cites work: Q4050946
cites work: Q4075816
cites work: Integral Averages and the Oscillation of Second Order Ordinary Differential Equations
DOI: 10.1006/JMAA.1997.5378
description: scientific article; zbMATH DE number 1031640