LAUSR

Abstract Consider the first-order linear differential equation with several non-monotone retarded arguments x ′ ⁢ ( t ) + ∑ i = 1 m p i ⁢ ( t ) ⁢ x ⁢ ( τ i ⁢ ( t ) ) = 0 {x^{\prime}(t)+\sum_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0} , t ≥ t 0 {t\geq t_{0}} , where the functions p i , τ i ∈ C ⁢ ( [ t 0 , ∞ ) , ℝ + ) {p_{i},\tau_{i}\in C([t_{0},\infty),\mathbb{R}^{+})} , for every i = 1 , 2 , … , m {i=1,2,\ldots,m} , τ i ⁢ ( t ) ≤ t {\tau_{i}(t)\leq t} for t ≥ t 0 {t\geq t_{0}} and lim t → ∞ ⁡ τ i ⁢ ( t ) = ∞ {\lim_{t\to\infty}\tau_{i}(t)=\infty} . New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.