NECESSARY AND SUFFICIENT CONDITIONS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATIONS

Abstract

In this work, we establish the necessary and sufficient conditions for oscillation of a class of functional differential equations of the form
((x(t) + p(t)x(t − σ))0 + q(t)φ(x(t − τ )) + v(t)ψ(x(t − η)) = 0 of a neutral coefficient p(t), by using the Knaster-Tarski fixed point theorem and Banach’s fixed point theorem.