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1996-1997 | 65 | 3 | 271-281
Tytuł artykułu

Stabilization of solutions to a differential-delay equation in a Banach space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
65
Numer
3
Strony
271-281
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-06-19
poprawiono
1996-10-17
Twórcy
autor
  • Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
  • Mathematical Institute, Academy of Sciences of The Czech Republic, 11567 Praha 1, Czech Republic
Bibliografia
  • [1] J. K. Hale, Theory of Functional Differential Equations, Springer, New York, 1977.
  • [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.
  • [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.
  • [4] S. Murakami, Stable equilibrium point of some diffusive functional differential equations, Nonlinear Anal. 25 (1995), 1037-1043.
  • [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.
  • [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.
  • [8] T. Wang, Stability in abstract functional differential equations. Part I. General theorems, J. Math. Anal. Appl. 186 (1994), 534-558.
  • [9] T. Wang, Stability in abstract functional differential equations, Part II. Applications, J. Math. Anal. Appl. 186 (1994), 835-861.
  • [10] G. F. Webb, Asymptotic stability for abstract nonlinear functional differential equations, Proc. Amer. Math. Soc. 54 (1976), 225-230.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv65z3p271bwm
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