Oscillation theorems for advanced differential equations


Amin Benaissa Cherif, Moussa Fethallah, Fatima Zohra Ladrani




In this paper, we will establish some oscillation criteria for the advanced differential equations u ′ (t) − i=k i=1 qi (t) u α (τi (t)) = 0, for t ≥ t0 where k is an integer and α is a quotient of odd integers, such as k ≥ 1 and α ≥ 1. The functions {qi} i∈{1,...,k} are continuous positive functions and the arguments {τi} i∈{1,...,k} are continuous positive functions, such that τi (t) > t, for i ∈ {1, ..., k}. This study aims to present some new sufficient conditions for the oscillation of solutions to a class of first-order advanced differential equations, using a technique based on a recursive sequence.