Oscillation and nonoscillation criteria for linear dynamic systems on time scales

Oscillation and Nonoscillation Criteria for Nonlinear Dynamic Systems on Time Scales

On oscillation and nonoscillation of second-order dynamic equations

New oscillation and nonoscillation criteria are established for second order linear equations with damping and forcing terms. Examples are given to illustrate the results.

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...

Half-Linear Dynamic Equations

Abstract. We survey half-linear dynamic equations on time scales. These contain the well-known half-linear differential and half-linear difference equations as special cases, but also other kinds of half-linear equations. Special cases of half-linear equations are the well-studied linear equations of second order. We discuss existence and uniqueness of solutions of corresponding initial value p...

Oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales

We obtain Willett-Wong-type oscillation and nonoscillation theorems for second order linear dynamic equations with integrable coefficients on a time scale. The results obtained extend and are motivated by oscillation and nonoscillation results due to Willett [20] and Wong [21] for the second order linear differential equation. As applications of the new results obtained, we give the complete cl...