Oscillation of second-order nonlinear delay dynamic equations on time scales. (English) Zbl 1075.34061

Summary: We establish the equivalence of the oscillation of the nonlinear dynamic equations \[ x^{\Delta\Delta}(t)+p(t)f\bigl(x(t-\tau) \bigr)=0\quad\text{and }x^{\Delta\Delta}(t)+p(t)(f\circ x^\sigma)=0 \] on time scales, from which we obtain some oscillation criteria and comparison theorems for the first equation. Next, we obtain some new oscillation criteria for second-order linear dynamic equations on time scales.


34K11 Oscillation theory of functional-differential equations
39A12 Discrete version of topics in analysis
34C41 Equivalence and asymptotic equivalence of ordinary differential equations
Full Text: DOI


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