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Oscillation criteria for third order nonlinear delay dynamic equations on time scales

Zhenlai Han, Tongxing Li, Shurong Sun, Fengjuan Cao (2010)

Annales Polonici Mathematici

By means of Riccati transformation technique, we establish some new oscillation criteria for third-order nonlinear delay dynamic equations ( ( x Δ Δ ( t ) ) γ ) Δ + p ( t ) x γ ( τ ( t ) ) = 0 on a time scale ; here γ > 0 is a quotient of odd positive integers and p a real-valued positive rd-continuous function defined on . Our results not only extend and improve the results of T. S. Hassan [Math. Comput. Modelling 49 (2009)] but also unify the results on oscillation of third-order delay differential equations and third-order delay difference...

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

Thandapani, E., Pandian, S., Revathi, T. (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 39A10.The oscillatory and nonoscillatory behaviour of solutions of the second order quasi linear neutral delay difference equation Δ(an | Δ(xn+pnxn-τ)|α-1 Δ(xn+pnxn-τ) + qnf(xn-σ)g(Δxn) = 0 where n ∈ N(n0), α > 0, τ, σ are fixed non negative integers, {an}, {pn}, {qn} are real sequences and f and g real valued continuous functions are studied. Our results generalize and improve some known results of neutral delay difference equations.

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