Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

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...

Nonoscillation Criteria for Nonlinear Delay Dynamic Systems on Time Scales

In this paper, we consider the nonlinear delay dynamic system x(t) = p(t)f1(y(t)), y (t) = −q(t)f2(x(t− τ)). We obtain some necessary and sufficient conditions for the existence of nonoscillatory solutions with special asymptotic properties of the system. We generalize the known results in the literature. One example is given to illustrate the results.

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

On oscillatory behavior of two-dimensional time scale systems

where a,b ∈ Crd([t0,∞)T,R+), and f and g are nondecreasing functions such that uf (u) > 0 and ug(u) > 0 for u = 0. The time scale theory is initiated by the German mathematician S. Hilger in his PhD thesis in 1988. His purpose was to unify continuous and discrete analysis and extend the results in one theory. A time scale, denoted by T, is a nonempty closed subset of real numbers, and some exam...