New product-type oscillation criteria for first-order linear differential equations with several nonmonotone arguments

We use an improved technique to establish new sufficient criteria of product type for the oscillation of the delay differential equation x ′ ( t ) + ∑ l = 1 m b l ( t ) x ( σ l ( t ) ) = 0 , t ≥ t 0 , with b l , σ l ∈ C ( [ t 0 , ∞ ) , [ 0 , ∞ ) ) such that σ l ( t ) ≤ t and lim t → ∞ σ l ( t ) = ∞ , l = 1 , 2 , … , m . The obtained results are applicable for the nonmonotone delay case. Their strength is supported by a detailed practical example.