We study scalar first order linear autonomous neutral delay differential equations with distributed type delays. This article presents some new results on the asymptotic behavior, the nonoscillation and the stability. These results are obtained via a real root (with an appropriate property) of the characteristic equation. Applications to the special cases such as (non-neutral) delay differentia...

The propose of the paper is devoted to study existence ?-periodic solutions for second order delay differential equation in abstract Banach space. Firstly, we build a new maximum principle corresponding linear equation. Secondly, with help this principle, minimal and maximal periodic our concerns problem by means perturbation method monotone iterative technique lower upper solutions. In additio...

This paper studies the asymptotic behavior of solutions of the second-order nonlinear delay differential equations with impulses: 1 ( ( ) ( )) ( ) ( ) ( ) ( ) ( ) 0 n i i k i r t x t p t x t q t x t f t t t σ ′ ′ ′ = − + − + = , ≠ , ∑ ( ) ( ) ( ) ( ) ( ) ( ) k k k k k k k k x t x t a x t x t x t b x t k Z ′ ′ ′ + + + − = , − = , ∈ . and some sufficient conditions are obtained. Keywords-Asymptot...