Semigroups and stability of nonautonomous differential equations in Banach spaces
HTML articles powered by AMS MathViewer
- by Nguyen Van Minh PDF
- Trans. Amer. Math. Soc. 345 (1994), 223-241 Request permission
Abstract:
This paper is concerned with nonautonomous differential equations in Banach spaces. Using the theory of semigroups of linear and nonlinear operators one investigates the semigroups of weighted translation operators associated with the underlying equations. Necessary and sufficient conditions for different types of stability are given in terms of spectral properties of the translation operators and the differential operators associated with the equations.References
-
B. Aulbach, Nguyen Van Minh, and P. P. Zabreiko, A generalization of monodromy operator and its applications, preprint.
- Charles J. K. Batty and Vũ Quốc Phóng, Stability of individual elements under one-parameter semigroups, Trans. Amer. Math. Soc. 322 (1990), no. 2, 805–818. MR 1022866, DOI 10.1090/S0002-9947-1990-1022866-5
- 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
- Ju. L. Dalec′kiĭ and M. G. Kreĭn, Stability of solutions of differential equations in Banach space, Translations of Mathematical Monographs, Vol. 43, American Mathematical Society, Providence, R.I., 1974. Translated from the Russian by S. Smith. MR 0352639
- 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
- José Luis Massera and Juan Jorge Schäffer, Linear differential equations and function spaces, Pure and Applied Mathematics, Vol. 21, Academic Press, New York-London, 1966. MR 0212324 Nguyen Van Minh, Semigroups and linear nonautonomous differential equations on the half line, Dokl. Akad. Sci. Belarus 37 (1992), no. 1, 19-22. (Russian)
- Nguen Van Min′, Nonlinear semigroups and nonlinear nonautonomous ordinary differential equations, Dokl. Akad. Nauk Belarusi 37 (1993), no. 2, 113–117, 219 (Russian, with English and Russian summaries). MR 1235213 K. Yosida, Functional analysis, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. P. P. Zabreiko and Nguyen Van Minh, Group of characteristic operators and its applications in the theory of linear differential equations, Dokl. Russian Acad. Sci. 324 (1992), no. 1, 24-28. (Russian)
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 345 (1994), 223-241
- MSC: Primary 34G10; Secondary 34D05, 34G20, 47D06, 47H20, 47N20
- DOI: https://doi.org/10.1090/S0002-9947-1994-1242785-2
- MathSciNet review: 1242785