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Asymptotic stability for abstract nonlinear functional differential equations. (English) Zbl 0324.34079


MSC:

34K20 Stability theory of functional-differential equations
47J05 Equations involving nonlinear operators (general)
34D20 Stability of solutions to ordinary differential equations
34G99 Differential equations in abstract spaces
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[1] 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. · Zbl 0226.47038 · doi:10.2307/2373376
[2] Michael G. Crandall and Amnon Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Functional Analysis 3 (1969), 376 – 418. · Zbl 0182.18903
[3] H. Flaschka and M. J. Leitman, On semigroups of nonlinear operators and the solution of the functional differential equation \?(\?)=\?(\?_{\?}), J. Math. Anal. Appl. 49 (1975), 649 – 658. · Zbl 0321.47046 · doi:10.1016/0022-247X(75)90204-8
[4] Jack K. Hale, Functional differential equations, Analytic theory of differential equations (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich., 1970) Springer, Berlin, 1971, pp. 9 – 22. Lecture Notes in Mat., Vol. 183.
[5] 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. · Zbl 0078.10004
[6] Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508 – 520. · Zbl 0163.38303 · doi:10.2969/jmsj/01940508
[7] C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc. 200 (1974), 395 – 418. · Zbl 0299.35085
[8] G. F. Webb, Autonomous nonlinear functional differential equations and nonlinear semigroups, J. Math. Anal. Appl. 46 (1974), 1 – 12. · Zbl 0277.34070 · doi:10.1016/0022-247X(74)90277-7
[9] -, Functional differential equations and nonlinear semigroups in \( {L^p}\)-spaces, J. Differential Equations (to appear).
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