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 ′ ) +X N j=0 qj (t)φαj (x) = e(t), where φα (u) := |u| α sgn u, 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.