Asymptotic behavior of third-order differential equations with nonpositive neutral coefficients and distributed deviating arguments

Abstract

Using the Riccati transformation technique, we present several sufficient conditions that guarantee that all solutions to a third-order differential equation with nonpositive neutral coefficients and distributed deviating arguments are either oscillatory or converge to zero asymptotically. In particular, we establish Hille and Nehari type criteria. Two examples are given to demonstrate the practicability of the main results.