On the distance between consecutive zeros of solutions of first order delay differential equations

This paper is concerned with the distribution of zeros of solutions of first order linear delay differential equations with variable coefficients of the formx′(t)+p(t)x(t-τ)=0,t⩾t∗,where τ>0, p(t)∈C([t∗,∞),[0,∞)). By introducing a class of polynomial functions, we are able to derive new estimates for the lower and upper bounds of the distance between consecutive zeros of solutions of the above equations. We illustrate the obtained results with several examples.