INTERVAL CRITERIA FOR FORCED OSCILLATION OF DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN, DAMPING, AND MIXED NONLINEARITIES

We consider forced second order differential equation with p-Laplacian and damping in the form of (r(t)φα0 (x )) ′ + p(t)φα0 (x ) + N ∑ j=0 qj(t)φαj (x) = e(t), where φα (u) := |u| α sgnu, αj > 0, j = 0, 1, 2, . . . , N , and r, p, qj , e ∈ C ([0,∞), R) with r (t) > 0 on [0,∞). Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. Our work generalizes, unifies, and improves many existing results in the literature. AMS (MOS) Subject Classification. 34C10, 34C15.

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