Oscillation criteria 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 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

Oscillation and Nonoscillation Criteria for Two-dimensional Time-scale Systems of First-order Nonlinear Dynamic Equations

Oscillation criteria for two-dimensional difference and differential systems of first-order linear difference equations are generalized and extended to nonlinear dynamic equations on arbitrary time scales. This unifies and extends under one theory previous linear results from discrete and continuous systems. An example is given illustrating that a key theorem is sharp on all time scales. 1. pre...