Title: Interval oscillation for second order sublinear differential equations with a damping term

Authors: Elmetwally M. Elabbasy, Taher S. Hassan

Addresses: Faculty of Science, Department of Mathematics, Mansoura University, Mansoura, 35516, Egypt. ' Faculty of Science, Department of Mathematics, Mansoura University, Mansoura, 35516, Egypt

Abstract: We present new oscillation criteria for the second order nonlinear differential equation with a damping term (a(t)y′(t))′ + p(t)y′(t) + q(t)|y(t)|^α−1y(t) = 0, t ≥ t₀ where 0 < α ≤ 1. Our results here are different, generalise and improve some known results for oscillation of second order nonlinear differential equations that are different from most known ones in the sencse they are based on the information only on a sequence of subintervals of [t₀, ∞), rather than on the whole half-line and can be applied to extreme cases such as ∫_t0^∞ q(t)dt = −∞. Our results are illustrated with examples.

Keywords: interval oscillation; second order differential equations; sublinear differential equations; damping terms.

DOI: 10.1504/IJDSDE.2008.023005

International Journal of Dynamical Systems and Differential Equations, 2008 Vol.1 No.4, pp.291 - 299

Published online: 06 Feb 2009 *

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