Oscillation of \(n\)th order equations with perturbations
type: Item
instance of: scholarly article
title: Oscillation of \(n\)th order equations with perturbations
zbMATH Open document ID: 0358.34031
DOI: 10.1016/0022-247X(77)90293-1
published in: Journal of Mathematical Analysis and Applications
publication date: 1977-01-01T00:00:00Z
review text: Two oscillation theorems are proved for the equation \[ x^{(n)}+H(t,x)=Q(t,x), \tag{1} \] \(n\) even. In Theorem 1 it is shown that if the homogeneous equation (2) \(x^{(n)}+H(t,x)=0\) boundedly oscillates and \[ |Q(t,x)|\leq Q_0(t)|x|^{r}, \] where \(r \geq 1\) and \(Q_0(t)\) is small, then every bounded solution of (1) oscillates. Theorem 2 relates the nonoscillatory solutions of (1) to a class of solutions of the equation \(y^{(n)} =Q(t,y)\). Thus, estimates on the growth of the nonoscillatory solutions of (1) are proved. Several examples are given to illustrate the theorems.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 3558250
author: Athanassios G. Kartsatos
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3558250