Asymptotic stability for abstract nonlinear functional differential equations
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- by G. F. Webb
- Proc. Amer. Math. Soc. 54 (1976), 225-230
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402237-0
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Abstract:
The nonlinear autonomous functional differential equation $\dot x(t) = f(x(t)) + g({x_t}),t \geqslant 0,{x_0} = \phi$ is investigated by means of the theory of semigroups of nonlinear operators. The properties of the semigroup associated with this equation provide stability information about the solutions.References
- M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265–298. MR 287357, DOI 10.2307/2373376
- Michael G. Crandall and Amnon Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Functional Analysis 3 (1969), 376–418. MR 0243383, DOI 10.1016/0022-1236(69)90032-9
- H. Flaschka and M. J. Leitman, On semigroups of nonlinear operators and the solution of the functional differential equation $\dot x(t)=F(x_{t})$, J. Math. Anal. Appl. 49 (1975), 649–658. MR 361959, DOI 10.1016/0022-247X(75)90204-8
- Jack K. Hale, Functional differential equations, Analytic theory of differential equations (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1970) Lecture Notes in Math., Vol. 183, Springer, Berlin, 1971, pp. 9–22. MR 0390425
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
- Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508–520. MR 226230, DOI 10.2969/jmsj/01940508
- C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395–418. MR 382808, DOI 10.1090/S0002-9947-1974-0382808-3
- G. F. Webb, Autonomous nonlinear functional differential equations and nonlinear semigroups, J. Math. Anal. Appl. 46 (1974), 1–12. MR 348224, DOI 10.1016/0022-247X(74)90277-7 —, Functional differential equations and nonlinear semigroups in ${L^p}$-spaces, J. Differential Equations (to appear).
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 225-230
- MSC: Primary 34K20; Secondary 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402237-0
- MathSciNet review: 0402237