Oscillation of second-order perturbed differential equations

Abstract

We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second-order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation, monotonicity of nonlinearity, and we establish global existence of oscillatory solutions without assuming it a priori. Furthermore, as our example demonstrates, existence of bounded oscillatory solutions does not exclude existence of unbounded nonoscillatory solutions. (c) 2005 WILEY-VCH Verlag GmbH & Co.