Abstract
We consider forced second order differential equation with p-Laplacian and nonlinearities given by a Riemann-Stieltjes integrals in the form of
(p(t)phi(gamma) (x'(t)))' + q(0) (t) phi(gamma) (x(t)) + integral(b)(0) q(t, s)phi(alpha(s)) (x(t)) d zeta (s) = e(t),
where phi(alpha) (u) := vertical bar u vertical bar(alpha) sgn u, gamma, b is an element of (0, infinity), alpha is an element of C [0, b) is strictly increasing such that 0 <= alpha (0) < gamma < alpha (b-), p, q(0), e is an element of C ([t(0), infinity), R) with p (t) >0 on [t(0), infinity), q is an element of C ([0, infinity) x [0, b)), and zeta : [0, b) -> R is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. As special cases, our work generalizes, unifies, and improves many existing results in the literature.