Oscillation of first order linear differential equations with several non-monotone delays

Abstract

Abstract Consider the first-order linear differential equation with several retarded arguments x ′ ( t ) + ∑ k = 1 n p k ( t ) x ( τ k ( t ) ) = 0 , t ≥ t 0 , $$\begin{array}{} \displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0}, \end{array} $$ where the functions pk , τk ∈ C([t 0, ∞), ℝ+), τk (t) < t for t ≥ t 0 and lim t→∞ τk (t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.