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A NONOSCILLATION THEOREM FOR SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DECAYING COEFFICIENTS

Published online by Cambridge University Press:  14 June 2001

JITSURO SUGIE
JITSURO SUGIE
Affiliation:
Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan; jsugie@math.shimane-u.ac.jp
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Abstract

The purpose of this paper is to give sufficient conditions for all nontrivial solutions of the nonlinear differential equation x″ +a(t)g(x) = 0 to be nonoscillatory. Here, g(x) satisfies the sign condition xg(x) > 0 if x ≠ 0, but is not assumed to be monotone increasing. This differential equation includes the generalized Emden–Fowler equation as a special case. Our main result extends some nonoscillation theorems for the generalized Emden–Fowler equation. Proof is given by means of some Liapunov functions and phase-plane analysis.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 3 , May 2001 , pp. 299 - 308
Copyright
© The London Mathematical Society 2001

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Footnotes

Research supported in part by Grant-in-Aid for Scientific Research 11304008.