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

Colloquium Mathematicae (1999)

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

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topSi, 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

top- [1] E. Eder, The functional differential equation ${x}^{\text{'}}\left(t\right)=x\left(x\left(t\right)\right)$, J. Differential Equations 54 (1984), 390-400. Zbl0497.34050
- [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. Zbl0892.30023
- [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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