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Oscillation and Existence of Positive Solutions for Odd-Order Neutral Equations with “Integrally Small” Coefficients

✍ Scribed by X.H. Tang; J.S. Yu

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
140 KB
Volume
222
Category
Article
ISSN
0022-247X

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✦ Synopsis

We establish several new sufficient conditions for the oscillation of all solutions Ž . and the existence of a positive solution when P t y 1 is allowed to oscillate and ϱ Ž . the usual divergent condition H Q s ds s ϱ is not satisfied. These conditions are almost sharp and improve some known results in the literature. Some examples are given to demonstrate the advantage of our results.

📜 SIMILAR VOLUMES

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Consider the higher order neutral differential equation x t y x t y q Ž . Ž . Ž . Q t x t y s 0, t G t with Q t continuous, ) 0, G 0, and n odd. We 0 establish several new sufficient conditions for the oscillation of all solutions and the existence of a positive solution by an associated ordinary di

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t ## Ž . , ␦ g R , G ␦ , are obtained where R t q H Q u du y 1 is allowed to x ϱ w Ž . Ž oscillate and the condition H s P s y Q s y q ␦ H P u y Q u y q t s 0 .x ␦ du ds s ϱ is not necessary. Some examples are given, which show that the results here are almost sharp.