Upper bounds for the distances between adjacent zeros of solutions of delay differential equations

This paper is concerned with upper bounds for the distances between adjacent 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 and p(t) ∈ C([t∗, ∞), R). By introducing a sequence of testing functions, we are able to derive upper bounds that are better than those in the literature.