This paper is concerned with a second-order functional differential equation of the form 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.
@article{bwmeta1.element.bwnjournal-article-cmv79z2p273bwm,
author = {Jian-Guo Si and Xin-Ping Wang},
title = {Analytic solutions of a second-order functional differential equation with a state derivative dependent delay},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {273-281},
zbl = {0927.34077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv79z2p273bwm}
}
Si, Jian-Guo; Wang, Xin-Ping. Analytic solutions of a second-order functional differential equation with a state derivative dependent delay. Colloquium Mathematicae, Tome 79 (1999) pp. 273-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv79z2p273bwm/
[000] [1] E. Eder, The functional differential equation , J. Differential Equations 54 (1984), 390-400. | Zbl 0497.34050
[001] [2] M. Kuczma, Functional Equations in a Single Variable, Polish Sci. Publ., Warszawa, 1968.
[002] [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. | Zbl 0892.30023
[003] [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. | Zbl 0872.34042