NEW CRITERIA FOR OSCILLATION OF SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH DAMPING ON TIME SCALES

Journal: IMPACT : International Journal of Research in Applied, Natural and Social Sciences ( IMPACT : IJRANSS ) (Vol.3, No. 3)

Publication Date: 2015-03-31

Authors : M. M. A. El-Sheikh; R. Sallam; Nahed A. Mohamady;

Page : 79-86

Keywords : Damped Delay Dynamic Equations; Oscillation Criteria; Time Scales;

Source : Download Find it from : Google Scholar

Abstract

The oscillation of solutions of the second order nonlinear damped dynamic equation (r(t)ψ (x(t))x^Δ (t))^Δ+ p(t)x^Δ (t) + f(t,x(τ (t))) = 0 on an arbitrary time scale T is investigated. A generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for the oscillation of solutions are obtained to extend some known results in the literature

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NEW CRITERIA FOR OSCILLATION OF SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH DAMPING ON TIME SCALES

Abstract

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