Analytic solutions of a second-order nonautonomous iterative functional differential equation

Analytic Solutions of a Second-Order Functional Differential Equation

Analytic solution of certain second-order functional differential equation

We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form x (x [r] (z)) = c 0 z 2 + c 1 (x(z)) 2 + (c 2 x [2] (z)) 2 + ··· + c m (x [m] (z)) 2 , m,r ≥ 0.

Periodic solutions for a second order nonlinear functional differential equation

The second order nonlinear delay differential equation with periodic coefficients x ′′(t)+ p(t)x ′(t)+ q(t)x(t) = r(t)x ′(t − τ(t))+ f (t, x(t), x(t − τ(t))), t ∈ R is considered in this work. By using Krasnoselskii’s fixed point theorem and the contraction mapping principle, we establish some criteria for the existence and uniqueness of periodic solutions to the delay differential equation. c ...

Analytic Solutions for Iterative Functional Differential Equations

Because of its technical difficulties the existence of analytic solutions to the iterative differential equation x′(z) = x(az + bx(z) + cx′(z)) is a source of open problems. In this article we obtain analytic solutions, using Schauder’s fixed point theorem. Also we present a unique solution which is a nonconstant polynomial in the complex field.

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations