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Function sequence technique for half-linear dynamic equations on time scales. (English) Zbl 1102.34020
Here, the author continues his earlier work on half-linear dynamic equations of the form $(r(t)\Phi(y^\Delta))^\Delta+p(t)\Phi(y^\sigma)=0$ on general time scales, where $$\Phi(u)=| u| ^{\alpha-1}\text{sgn}\,u$$, $$\alpha>1$$ and $$r,p$$ satisfy appropriate assumptions. This framework unifies the corresponding theories for half-linear ordinary differential and difference equations.
He develops a function sequence technique, which combined with corresponding Riccati techniques, can be applied to oscillation problems. In particular, various new oscillation/non-oscillation criteria of Hille-Nehari-, as well as of Willet-type are deduced. It is worth to point out that some of these conditions are new even in the classical cases of ODEs and difference equations. Several examples illustrate the results and show their applicability, where classical criteria may fail.

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 39A14 Partial difference equations 39A13 Difference equations, scaling ($$q$$-differences)