On the boundedness and oscillation of solutions to \((m(t)x^ 1)^ 1+a(t)b(x)=0\)
type: Item
instance of: scholarly article
title: On the boundedness and oscillation of solutions to \((m(t)x^ 1)^ 1+a(t)b(x)=0\)
zbMATH Open document ID: 0617.34026
DOI: 10.1155/S016117128700005X
author: Allan J. Kroopnick
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46169
review text: Conditions are given for the solutions of \((m(t)x')'+a(t)b(x)=0\) to be bounded, oscillatory and stable. Typically, the boundedness result is as follows. Suppose that a(t) and m(t) are \(C^ 1[0,\infty)\), and that \(a(t)\geq a_ 0\geq 0\) and \(m(t)\geq m_ 0\geq 0\) for some positive constants \(a_ 0\) and \(m_ 0\). Suppose also that m'(t)\(\leq 0\), a'(t)\(\leq 0\) and that \(b(x)\in C(-\infty,+\infty)\). If \(\lim_{| x| \to \infty}\int^{x}_{0}b(u)du=+\infty,\) then \(| x|\) and \(| x'|\) are bounded as \(t\to \infty\).
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4000422
zbMATH Keywords: oscillations
zbMATH Keywords: boundedness
MaRDI profile type: Publication
OpenAlex ID: W1514306248
description: scientific article; zbMATH DE number 4000422