Holomorphic solutions to functional differential equations

Singular Solutions and Prolongation of Holomorphic Solutions to Nonlinear Differential Equations

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Positive periodic solutions of functional differential equations

We consider the existence, multiplicity and nonexistence of positive o-periodic solutions for the periodic equation x0ðtÞ 1⁄4 aðtÞgðxÞxðtÞ lbðtÞf ðxðt tðtÞÞÞ; where a; bACðR; 1⁄20;NÞÞ are o-periodic, Ro 0 aðtÞ dt40; Ro 0 bðtÞ dt40; f ; gACð1⁄20;NÞ; 1⁄20;NÞÞ; and f ðuÞ40 for u40; gðxÞ is bounded, tðtÞ is a continuous o-periodic function. Define f0 1⁄4 limu-0þ f ðuÞ u ; fN 1⁄4 limu-N f ðuÞ u ; i0...

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.

Functional Differential Equations Close to Differential Equations

when the lag function r(t) is nearly constant for large /, and has also asked for conditions on the function r under which all solutions approach zero as t—» oo. The purpose of this announcement is to initiate a study of various stability and oscillation problems for equations with perturbed lag functions, and to suggest that a modification of the familiar method of conversion to an integral eq...