Oscillation criterion for two-dimensional dynamic systems on time scales

Oscillation 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.

Oscillation Theorems for Dynamic Equation on Time Scales

By using the generalized Riccati transformation and the inequality technique, we establish a oscillation criterion for certain non-linear secondorder dynamic equations with damping on a time scale.

Oscillation Criteria for Impulsive Dynamic Equations on Time Scales

Oscillation criteria for impulsive dynamic equations on time scales are obtained via impulsive inequality. An example is given to show that the impulses play a dominant part in the oscillations of dynamic equations on time scales.

Oscillation and nonoscillation criteria for linear dynamic systems on time scales

We consider the nonlinear dynamic system x Δ t atgyt, y Δ t −ft, x σ t. We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some examples are included to illustrate the results.

Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales