The Exist Local Analytic Solutions of an Iterative Functional Differential Equation

Local Analytic Solutions of an Iterative Functional Differential Equation Depend on the State Derivative

Analytic Solutions of an Iterative Functional Differential Equations Near Regular Points

l=0 |c l | < 1, and xl(z) = x(xl−1(z)) that denote the nth iterate of a map x. In general, F, G are given complex-valued functions of a complex variable. In this paper, analytic solutions of nonlinear iterative functional differential equations are investigated. Existence of locally analytic solutions and their construction is given in the case that all given functions exist regular points. As ...

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.

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

Analytic Solutions of an Iterative Functional Differential Equation with Delays Depending On State

This This paper is concerned with an iterative functional differential equation with the form C z z x b az x z x     ,)) ((1) (.By constructing a convergent power series solution of an auxiliary equation C z z g z ag z g z ag z g z g z g a b        ), ()] () ()][ () ([)] () ([ 2 2 2      the analytic solutions for the original equation are obtained. We not only discuss the cons...