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Oscillation for neutral dynamic functional equations on time scales. (English) Zbl 1060.34038

This paper is concerned with the neutral dynamic equation

(x(t)-P(t)x(g(t)) +Q(t)x(h(t))=0

on a time scale T. An interval condition is imposed on the neutral delay term g and on the nonneutral deviating argument term h that allows g(t) to be locally nonincreasing. The term h(t) can be delay, advanced, or h(t)-t can oscillate about zero. The influence of oscillation of P(t) is addressed along with a positive number for both regular and nonregular oscillation with respect to g(t). Results involve integrals of combinations of P,Q,g and h as well as auxiliary functions. Applications to difference equations are given.

MSC:
34K11Oscillation theory of functional-differential equations
34K40Neutral functional-differential equations
39A10Additive difference equations