Oscillation criteria for certain nonlinear differential equations. (English) Zbl 0921.34034

Rogovchenko, Yuri V.

J. Math. Anal. Appl. 229, No. 2, 399-416 (1999).

The author studies the second-order ordinary differential equation \[ x''(t)+p(t)f(x(t))g(x'(t))=0,\tag{1} \] and the delay differential equations \[ x''(t)+p(t)f(x(\tau (t)))g(x'(t))=0\tag{2} \] and \[ x''(t)+p(t)f(x(t),x(\tau (t)))g(x'(t))=0 \tag{3} \] for \(t\geq t_0\).
He obtains oscillation criteria for equations (1), (2) and (3), complements those given by S. R. Grace and B. S. Lalli [J. Math. Anal. Appl. 123, 584-588 (1987; Zbl 0641.34031)] and G.G. Hamedani and G.S. Krenz [J. Math. Anal. Appl. 149, No. 1, 271-276 (1990; Zbl 0701.34043)] and handles the cases which are not covered by known criteria. The results are obtained by using an integral averaging technique.

Reviewer: J.Ohriska (Košice)

MSC:

34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C29	Averaging method for ordinary differential equations

Keywords:

oscillation theory; nonlinear oscillations; averaging method

Citations:

Zbl 0641.34031; Zbl 0701.34043

References:

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