Necessary and Sufficient Conditions for Oscillation of Second Order Neutral Differential Equations

✍ Scribed by James S.W Wong

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 94 KB
• Volume: 252
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7063

✦ Synopsis

Consider the second order nonlinear neutral differential equation with delays: Ž .

w . E d rdt y t y py t y q q t f y t y s 0, for t g 0, ϱ , where Ž . Ž .

Ž . Ž . q t , f x are continuous functions, q t G 0, yf y ) 0 if y / 0, and 0p -1, Ž . ) 0, ) 0. When f y satisfies either the superlinear or sublinear conditions Ž . < < ␥y1 which include the special case f y s y y of ␥ ) 1 and 0 -␥ -1, respectively, we give necessary and sufficient conditions for the oscillation of all continu-Ž .

Ž . able solutions of E . When p s s s 0 in E , these results reduce to the well Ž . known theorems of Atkinson and Belohorec in the special case when f y s < < ␥y1 y y , ␥ / 1.