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Interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations. (English) Zbl 0983.34020

The authors consider the oscillation behavior of solutions to the second-order nonlinear differential equation \[ y''(t)+g(t)f(y(t))g(y'(t))=0,\quad t\geq t_0\in\mathbb{R}.\tag{1} \] Sufficient conditions for the solutions to (1) to be oscillatory are obtained. The authors give two examples to show that their results handle cases which are not covered by known results.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34C29 Averaging method for ordinary differential equations
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