Interval criteria for forced oscillation with nonlinearities given by Riemann-Stieltjes integrals
We study the oscillation of second-order forced differential equations with nonlinearity given by a Riemann-Stieltjes integral of the form (p(t)x')' + q(t)x + integral(b)(0) r(t, s)vertical bar x(t)vertical bar(alpha(s))sgnx(t)d xi(s) = e(t) where b is an element of (0, infinity], alpha is an element of C[0, b) is strictly increasing such that 0   0, r is an element of C([0, infinity) x [0, b)), and xi : [0, b) -> R is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. As a special case, the work in this paper unifies and improves the existing results in the literature for equations with a finite number of nonlinear terms. We also extend our results to equations with delays. (C) 2011 Elsevier Ltd. All rights reserved.
interval criteria forced oscillation riemann-stieltjes integral nonlinear differential equations