Analytic solutions of a first order iterative differential equation x'(z)=x(p(z) + bx(z))

• Autorzy: Qiu F. , Liu H.
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with a iterative differential equation x'{z) = x{p(z) + bx(z)). By constructing a convergent power series solution y(z) of a companion equation of the form betay'(3betaz) = y'(z)[y(beta2z) - p(y(betaz)]], analytic solutions of the form [y(betay- l(z)) - p(z)]/b for the original differential equation are obtained.

Słowa kluczowe

EN

analytic solution; functional equation; differential equations

PL

rozwiązania analityczne; równania funcjonalne; równania różniczkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 81--90
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Qiu F.

autor

Liu H.

• Department of Mathematics, Binzhou University 5th Yellow River Road Binzhou, Shandong.256600 P.R. China,

Bibliografia

• [1] E. Eder, The functional differential equation x'(z) = x(x(t)), J. Differential Equations 54 (1984), 390-400.
• [2] A. Elbert, Asymptotic behaviour of the analytic solution differential equation y'(t) +y(qt) = 0 as q ! 1-1, J. Comput. Appl. Math. 41 (1992), 5-22.
• [3] Jian-guo Si, Sui Sun Cheng, Analytic solutions of a functional differential equation with state dependent argument, Taiwanese J. Math. 1(4) (1997), 471-480.
• [4] Wen Rong Li and Sui Sun Cheng, Analytic solutions of an iterative functional equation, Journal of Binzhou Teachers College 19(2) (2003).
• [5] C. L. Siegel, Iterative of analytic function [J], Ann. of Math. 43(4) (1942), 607-612.