Pavel Řehák

Comparison theorems for linear dynamic equations on time scales

We obtain several comparison theorems for second order linear dynamic equations on a time scale. These results extend comparison theorems for the continuous case and provide some new results in the discrete case, as well as other more general situations.

Oscillatory Properties of Second Order Half-Linear Difference Equations

AbstractWe study oscillatory properties of the second order half-linear difference equation

Nonoscillation criteria for half-linear second-order difference equations

\Delta (r_k |\Delta yk|^{\alpha - 2} \Delta yk) - pk|yk + 1|^{\alpha - 2} yk + 1 = 0,\alpha > 1

How the constants in Hille-Nehari theorems depend on time scales

. It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation

On certain comparison theorems for half-linear dynamic equations on time scales

\Delta (r_k \Delta yk) - pkyk + 1 = 0.

q-regular variation and q-difference equations

. We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.