Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-21T21:51:53.126Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic linearity of solutions of nonlinear differential equations

Published online by Cambridge University Press:  17 April 2009

Shaozhu Chen
Shaozhu Chen
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 1A1.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we establish sufficient or necessary conditions for the nonlinear differential equation u″ + f (t, u) = 0 to have solutions which are asymptotic to lines with non-zero slopes and correct some formulations in theorems obtained by D.S. Cohen and J. Tong.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 2 , April 1987 , pp. 257 - 265
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Bellman, R., Stability theory of differential equations, McGraw-Hill, New York, 1953.Google Scholar
[2]Bihari, I., “A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations”, Acta Math. Acad. Sci. Hungar., 7 (1957), 81–94.CrossRefGoogle Scholar
[3]Cohen, D.S., “The asymptotic behaviour of a class of nonlinear differential equations”, Proc.Amer.Math.Soc., 18 (1967), 607–609.CrossRefGoogle Scholar
[4]Hille, E., “Nonoscillation theorems”, Trans.Amer.Math.Soc., 64 (1948), 234–252.CrossRefGoogle Scholar
[5]Tong, J., “The asymptotic behaviour of a class of nonlinear differential equations of second order”, Proc.Amer.Math.Soc., 84 (1982), 235–236.CrossRefGoogle Scholar