Analytic solutions of a second-order functional differential equation with a state derivative dependent delay

• Autorzy: Jian-Guo Si , Xin-Ping Wang
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with a second-order functional differential equation of the form $x''(z)=x(az+bx'(z))$ with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.

Słowa kluczowe

EN

analytic solution; functional differential equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 79
• Numer: 2
• Strony: 273-281

Daty

wydano

1999

otrzymano

1998-07-15

poprawiono

1998-09-27

Twórcy

autor

Jian-Guo Si

• Department of Mathematics, Binzhou Normal College, Binzhou, Shandong 256604, P.R. China

autor

Xin-Ping Wang

• Department of Mathematics, Binzhou Normal College, Binzhou, Shandong 256604, P.R. China

Bibliografia

• [1] E. Eder, The functional differential equation $x'(t)=x(x(t))$, J. Differential Equations 54 (1984), 390-400.
• [2] M. Kuczma, Functional Equations in a Single Variable, Polish Sci. Publ., Warszawa, 1968.
• [3] J. G. Si and S. S. Cheng, Analytic solutions of a functional differential equation with state dependent argument, Taiwanese J. Math. 1 (1997), 471-480.
• [4] J. G. Si, W. R. Li and S. S. Cheng, Analytic solutions of an iterative functional differential equation, Comput. Math. Appl. 33 (1997), no. 6, 47-51.