On the number of zeros of nonoscillatory solutions to half-linear ordinary differential equations involving a parameter

Authors:
Kusano Takasi and Manabu Naito

Journal:
Trans. Amer. Math. Soc. **354** (2002), 4751-4767

MSC (2000):
Primary 34C10; Secondary 34B16

DOI:
https://doi.org/10.1090/S0002-9947-02-03079-9

Published electronically:
July 8, 2002

MathSciNet review:
1926835

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the following half-linear ordinary differential equation is considered:

where is a constant, is a parameter, and is a continuous function on , , and for . The main purpose is to show that precise information about the number of zeros can be drawn for some special type of solutions of (H such that

It is shown that, if and if (H is strongly nonoscillatory, then there exists a sequence such that , as ; and with has exactly zeros in the interval and ; and with has exactly zeros in and . For the proof of the theorem, we make use of the generalized Prüfer transformation, which consists of the generalized sine and cosine functions.

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Additional Information

**Kusano Takasi**

Affiliation:
Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan

Email:
tkusano@cis.fukuoka-u.ac.jp

**Manabu Naito**

Affiliation:
Department of Mathematical Sciences, Faculty of Science, Ehime University, Matsuyama 790-8577, Japan

Email:
mnaito@math.sci.ehime-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-02-03079-9

Keywords:
Half-linear equations,
zeros of nonoscillatory solutions

Received by editor(s):
January 5, 2001

Published electronically:
July 8, 2002

Article copyright:
© Copyright 2002
American Mathematical Society