On the oscillatory behavior of volterra integral equations on time-scales

Abstract

The authors establish some new criteria for the oscillation of the Volterra integral equation on a time-scale x(t) = e(t) - ∫t 0 k(t, s)f(s,x(s))δs, for t > 0. They apply a technique that allows them to employ Gronwall's inequality instead of a Bihari inequality. The results obtained extend some existing results in the literature.