Taiwanese Journal of Mathematics

ANALYTIC SOLUTIONS OF A FUNCTIONAL DIFFERENTIAL EQUATION WITH STATE DEPENDENT ARGUMENT

Jian-Guo Si and Sui Sun Cheng

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Abstract

This paper is concerned with a functional differential equation $x'(z) = x(az + bx(z))$, where $a \neq 1$ and $b \neq 0$. By constructing a convergent power series solution $y(z)$ of a companion equation of the form $\beta y'(\beta z) = y'(z) [y (\beta ^2z) - ay(\beta z) + a]$, analytic solutions of the form $(y (\beta y^{-1} (z)) - az) /b$ for the original differential equation are obtained.

Article information

Source
Taiwanese J. Math., Volume 1, Number 4 (1997), 471-480.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406123

Digital Object Identifier
doi:10.11650/twjm/1500406123

Mathematical Reviews number (MathSciNet)
MR1486566

Zentralblatt MATH identifier
0892.30023

Subjects
Primary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 34K25: Asymptotic theory

Keywords
functional differential equation analytic solution

Citation

Si, Jian-Guo; Cheng, Sui Sun. ANALYTIC SOLUTIONS OF A FUNCTIONAL DIFFERENTIAL EQUATION WITH STATE DEPENDENT ARGUMENT. Taiwanese J. Math. 1 (1997), no. 4, 471--480. doi:10.11650/twjm/1500406123. https://projecteuclid.org/euclid.twjm/1500406123


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