Kamenev-Type Oscillation Criteria for Higher-Order Neutral Delay Dynamic Equations
نویسندگان
چکیده
In this paper, we are primarily concerned with the oscillation of solutions to higher-order dynamic equations. We first extend some recent results which have been obtained for second-order dynamic equations to even-order neutral delay dynamic equations. Our technique depends on making use of the Riccati substitution and the use of properties of the generalized Taylor monomials on time scales. We also extend our results to odd-order neutral delay dynamic equations. Some examples for differential equations, difference equations, and q-difference equations (which have important applications in quantum theory) are given to illustrate the results obtained. AMS Subject Classifications: 34K11, 39A10.
منابع مشابه
Oscillation of Nonlinear Neutral Delay Differential Equations of Second Order
Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...
متن کاملOscillation of second order neutral equations with distributed deviating argument
Oscillation criteria are established for the second order neutral delay differential equation with distributed deviating argument (r(t) (x(t))Z′(t))′ + ∫ b a q(t, )f [x(g(t, ))] d ( )= 0, t t0, where Z(t)= x(t)+p(t)x(t − ). These results are extensions of the integral averaging techniques due to Coles and Kamenev, and improve some known oscillation criteria in the existing literature. © 2006 El...
متن کاملDynamic Systems and Applications 17 (2008) 551-570 OSCILLATION OF SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES
By using the functions of the form H(t, s) and a generalized Riccati technique, we establish new Kamenev-type and interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form ( p(t)x(t) )∆ + f(t, x(σ(t))) = 0. The obtained interval oscillation criteria can be applied to equations with forcing term. Two examples are included to show the significance of th...
متن کاملKamenev-type Oscillation Criteria for Second-order Quasilinear Differential Equations
We obtain Kamenev-type oscillation criteria for the second-order quasilinear differential equation (r(t)|y′(t)|α−1y′(t))′ + p(t)|y(t)|β−1y(t) = 0 . The criteria obtained extend the integral averaging technique and include earlier results due to Kamenev, Philos and Wong.
متن کامل