Stabilization of solutions to a differential-delay equation in a Banach space
Annales Polonici Mathematici (1997)
- Volume: 65, Issue: 3, page 271-281
- ISSN: 0066-2216
Access Full Article
top
Abstract
topHow to cite
topJ. J. Koliha, and Ivan Straškraba. "Stabilization of solutions to a differential-delay equation in a Banach space." Annales Polonici Mathematici 65.3 (1997): 271-281. <http://eudml.org/doc/269978>.
@article{J1997,
abstract = {A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.},
author = {J. J. Koliha, Ivan Straškraba},
journal = {Annales Polonici Mathematici},
keywords = {abstract differential-delay equation; dependence on parameter; uniform stability; differential delay equations; linearized stability},
language = {eng},
number = {3},
pages = {271-281},
title = {Stabilization of solutions to a differential-delay equation in a Banach space},
url = {http://eudml.org/doc/269978},
volume = {65},
year = {1997},
}
TY - JOUR
AU - J. J. Koliha
AU - Ivan Straškraba
TI - Stabilization of solutions to a differential-delay equation in a Banach space
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 3
SP - 271
EP - 281
AB - A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.
LA - eng
KW - abstract differential-delay equation; dependence on parameter; uniform stability; differential delay equations; linearized stability
UR - http://eudml.org/doc/269978
ER -
References
top- [1] J. K. Hale, Theory of Functional Differential Equations, Springer, New York, 1977. Zbl0352.34001
- [2] J. S. Jung, J. Y. Park and H. J. Kang, Asymptotic behavior of solutions of nonlinear functional differential equations, Internat. J. Math. Math. Sci. 17 (1994), 703-712. Zbl0816.47070
- [3] J. J. Koliha and I. Straškraba, Stability in nonlinear evolution problems by means of fixed point theorems, Comment. Math. Univ. Carolin. 38 (1) (1997), to appear. Zbl0891.34065
- [4] S. Murakami, Stable equilibrium point of some diffusive functional differential equations, Nonlinear Anal. 25 (1995), 1037-1043. Zbl0841.35121
- [5] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
- [6] C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395-418. Zbl0299.35085
- [7] C. C. Travis and G. F. Webb, Partial differential equations with deviating arguments in the time variable, J. Math. Anal. Appl. 56 (1976), 397-409. Zbl0349.35071
- [8] T. Wang, Stability in abstract functional differential equations. Part I. General theorems, J. Math. Anal. Appl. 186 (1994), 534-558. Zbl0814.34066
- [9] T. Wang, Stability in abstract functional differential equations, Part II. Applications, J. Math. Anal. Appl. 186 (1994), 835-861. Zbl0822.34065
- [10] G. F. Webb, Asymptotic stability for abstract nonlinear functional differential equations, Proc. Amer. Math. Soc. 54 (1976), 225-230. Zbl0324.34079
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.