Dynamic Systems and Applications 17 (2008) 551-570 OSCILLATION OF SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES
نویسنده
چکیده
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 the results. AMS (MOS) Subject Classification. 39A10, 34C10
منابع مشابه
Forced Oscillation of Second Order Nonlinear Dynamic Equations on Time Scales
By means of the Kartsatos technique and generalized Riccati transformation techniques, we establish some new oscillation criteria for a second order nonlinear dynamic equations with forced term on time scales in terms of the coefficients.
متن کاملOscillation of Second-order Nonlinear Impulsive Dynamic Equations on Time Scales
In this article, we study the oscillation of second-order nonlinear impulsive dynamic equations on time scales. Using Riccati transformation techniques, we obtain sufficient conditions for oscillation of all solutions. An example is given to show that the impulses play a dominant part in oscillations of dynamic equations on time scales.
متن کاملFirst order linear fuzzy dynamic equations on time scales
In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.
متن کاملOscillation of Second Order Nonlinear Dynamic Equations on Time Scales
By means of Riccati transformation techniques, we establish some oscillation criteria for a second order nonlinear dynamic equation on time scales in terms of the coefficients. We give examples of dynamic equations to which previously known oscillation criteria are not applicable.
متن کاملOscillation criteria for nonlinear damped dynamic equations on time scales
We present new oscillation criteria for the second order nonlinear damped delay dynamic equation (r(t)(x(t))) + p(t)(x(t)) + q(t)f (x(τ(t))) = 0. Our results generalize and improve some known results for oscillation of second order nonlinear delay dynamic equation. Our results are illustrated with examples.
متن کامل