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On the stability of nonlinear operator differential equations, and applications. (English) Zbl 0187.08801


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[1] Browder, F. E., Nonlinear equations of evolution. Ann. of Math. 80, 485–523 (1964). · Zbl 0127.33602 · doi:10.2307/1970660
[2] Browder, F. E., Nonlinear equations of evolution and nonlinear accretive operators in Banach spaces. Bull. Amer. Math. Soc. 73, 867–874 (1967). · Zbl 0176.45301 · doi:10.1090/S0002-9904-1967-11820-2
[3] Buis, G. R., Lyapunov Stability for Partial Differential Equations. Part I, NASA CR-1100, 1968.
[4] Dunford, N., & J. Schwartz, Linear Operators. Vol. 1. New York: Interscience 1963. · Zbl 0128.34803
[5] Kato, T., Nonlinear semi-groups and evolutions equations. J. Math. Soc. Japan 19, 508–520 (1967). · Zbl 0163.38303 · doi:10.2969/jmsj/01940508
[6] Kōmura, Y., Nonlinear semi-groups in Hilbert space. J. Math. Soc. Japan 19, 493–507 (1967). · Zbl 0163.38302 · doi:10.2969/jmsj/01940493
[7] Lumer, G., & R. S. Phillips, Dissipative operators in a Banach space. Pacific J. Math. 11, 679–698 (1961). · Zbl 0101.09503 · doi:10.2140/pjm.1961.11.679
[8] Minty, G. J., Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29, 341–346 (1962). · Zbl 0111.31202 · doi:10.1215/S0012-7094-62-02933-2
[9] Pao, C. V., The Existence and Stability of Solutions to Nonlinear Operator Differential Equations. Preceding in this issue. · Zbl 0187.08702
[10] Vogt, W. G., M. M. Eisen, & G. R. Buis, Contraction groups and equivalent norms. Nagoya Math. J. 34 (to appear); also Lyapunov Stability for Partial Differential Equations. Part II, NASA CR-1100, 1968.
[11] Yosida, K., Functional Analysis. Berlin-Heidelberg-New York: Springer 1966. · Zbl 0152.32102
[12] Zubov, V. I., Methods of A. M.Lyabunov and their Application. The Netherlands: P. Noordhoff Ltd. 1964.
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