Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-01T21:05:00.424Z Has data issue: false hasContentIssue false
  • English
  • Français

On uniqueness and continuability of the Emden–Fowler equation

Published online by Cambridge University Press:  09 April 2009

Man Kam Kwong
Man Kam Kwong
Affiliation:
Hong Kong Baptist College, 224, Waterloo Road, Kowloon, Hong Kong.
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.

The Emden-Fowler equation x″(t) + a(t)|x|γ sgn x = 0, t ≧ 0, is said to be in the sublinear or superlinear case according to whether γ < 1 or γ > 1. Conditions on a(t) are given to ensure local uniqueness of solutions in the sublinear case and continuability of solutions in the superlinear case. Boundedness of solutions is also studied.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1977 , pp. 121 - 128
Copyright
Copyright © Australian Mathematical Society 1977

References

Coffman, C. V. and Wong, J. S. W. (1972), ‘Oscillation and nonoscillation of soluions of generagized Emden-Fowler equation’, Trans. Amer. Math. Soc., 167, 399–434.CrossRefGoogle Scholar
Heidel, J. W. (1970), ‘Uniqueness, continuation and nonoscillation for a second order non-linear differential equation’, Pacific J. Math., 32, 715–721.CrossRefGoogle Scholar
Wong, J. S. W. (1973), ‘On the generalized Emden-Fowler equation’, Report Center for Theoretical Studies, University of Miami.Google Scholar
Wong, J. S. W. (1967), ‘Explicit bounds for solutions of certain second order non-linear differential equations’, J. Math. Anal. Appl., 17, 339–342.CrossRefGoogle Scholar