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

Jian-Guo Si; Xin-Ping Wang

Colloquium Mathematicae (1999)

  • Volume: 79, Issue: 2, page 273-281
  • ISSN: 0010-1354

Abstract

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This paper is concerned with a second-order functional differential equation of the form x ' ' ( z ) = x ( a z + b x ' ( 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.

How to cite

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Si, Jian-Guo, and Wang, Xin-Ping. "Analytic solutions of a second-order functional differential equation with a state derivative dependent delay." Colloquium Mathematicae 79.2 (1999): 273-281. <http://eudml.org/doc/210641>.

@article{Si1999,
abstract = {This paper is concerned with a second-order functional differential equation of the form $x^\{\prime \prime \}(z)=x(az+bx^\{\prime \}(z))$ 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.},
author = {Si, Jian-Guo, Wang, Xin-Ping},
journal = {Colloquium Mathematicae},
keywords = {analytic solution; functional differential equation; functional-differential equation; analytic solutions},
language = {eng},
number = {2},
pages = {273-281},
title = {Analytic solutions of a second-order functional differential equation with a state derivative dependent delay},
url = {http://eudml.org/doc/210641},
volume = {79},
year = {1999},
}

TY - JOUR
AU - Si, Jian-Guo
AU - Wang, Xin-Ping
TI - Analytic solutions of a second-order functional differential equation with a state derivative dependent delay
JO - Colloquium Mathematicae
PY - 1999
VL - 79
IS - 2
SP - 273
EP - 281
AB - This paper is concerned with a second-order functional differential equation of the form $x^{\prime \prime }(z)=x(az+bx^{\prime }(z))$ 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.
LA - eng
KW - analytic solution; functional differential equation; functional-differential equation; analytic solutions
UR - http://eudml.org/doc/210641
ER -

References

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  1. [1] E. Eder, The functional differential equation x ' ( t ) = x ( x ( t ) ) , J. Differential Equations 54 (1984), 390-400. Zbl0497.34050
  2. [2] M. Kuczma, Functional Equations in a Single Variable, Polish Sci. Publ., Warszawa, 1968. 
  3. [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. Zbl0892.30023
  4. [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. Zbl0872.34042

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