Analytic solutions of a second-order functional differential equation with a state derivative dependent delay

Analytic Solutions of a First Order Functional Differential Equation with a State Derivative Dependent Delay

This article concerns the first-order functional differential equation x′(z) = x(p(z) + bx′(z)) with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.

Existence of Solutions for a Second Order Abstract Functional Differential Equation with State-dependent Delay

In this paper we study the existence of mild solutions for abstract partial functional differential equation with state-dependent delay.

Analytic Solutions of a Second-Order Functional Differential Equation

Existence Results for a Second Order Impulsive Functional Differential Equation with State–dependent Delay

In this paper, we study existence of mild solutions for a second order impulsive neutral functional differential equations with state-dependent delay. By using a fixed point theorem for condensing maps combined with theories of a strongly continuous cosine family of bounded linear operators, we prove the main existence theorems. As applications of these obtained results, some practical conseque...

Some Properties of Solutions of a Functional-Differential Equation of Second Order with Delay

Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov's fixed point theorem and weakly Picard operator theory.