Oscillation criteria for third-order semi-canonical differential equations with unbounded neutral coefficients

Abstract

In this paper, we investigate the oscillatory behavior of solutions to a class of third-order differential equations of the form Lz(t) + f (t)yβ (σ(t)) = 0, where Lz(t) = (p(t)(q(t)zt(t))t)t is a semi-canonical operator and z(t) = y(t) + g(t)y(τ (t)). The main idea is to convert the semi-canonical operator into canonical form and then obtain some new sufficient conditions for the oscillation of all solutions. The obtained results essentially improve and complement to the known results. Examples are provided to illustrate the main results. Mathematics Subject Classification (2010): 34C10, 34K11, 34K40. Received 19 September 2021; Accepted 20 January 2022