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

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.

### 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

### Citations:

Zbl 0641.34031; Zbl 0701.34043
Full Text:

### References:

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