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Stability theory and Lyapunov’s second method. (English) Zbl 0133.34902


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[1] Antosiewicz, H. A.: A Survey of Lyapunov’s Second Method. Contributions to the theory of non-linear oscillations 4, pp. 141–166, Ann of Math. Studies 41, Princeton Univ. Press, 1958. · Zbl 0082.30102
[2] Cesari, L.: Asymptotic Behavior and Stability Problems in Ordinary Differential Equations. Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., Heft 16. Berlin-Göttingen-Heidelberg: Springer 1959. · Zbl 0082.07602
[3] Lyapunov, A.: Problème général de la stabilité du mouvement. Ann. of Math. Studies 17, Princeton Univ. Press, 1947.
[4] Malkin, I.: On Stability in the First Approximation. Naucnyh Trudov Kazan. Aviacionnogo Inst. im. P. I. Baranova 3, 1934 [Russian].
[5] Malkin, I.: Certain Questions on the Theory of the Stability of Motion in the Sense of Liapounoff. Amer. Math. Soc. Translation, 20, 1950, – tr. from Sbornik Naucnyh Trudov Kazan. Aviacionnogo Inst. im. P.I. Baranova 7, 1937. · Zbl 0041.52801
[6] Malkin, I.: Verallgemeinerung des Fundamentalsatzes von Liapounoff über die Stabilität der Bewegungen. Dokl. Akad. Nauk SSSR 18, 162–164 (1938). · Zbl 0018.09502
[7] Malkin, I.: On the Question of the Reciprocal of Lyapunov’s Theorem on Asymptotic Stability. Prikl. Mat. Meh. 18, 129–138 (1954) [Russian].
[8] Massera, J. L.: On Liapounoff’s Conditions of Stability. Ann. of Math. (2) 50, 705–721 (1949). · Zbl 0038.25003 · doi:10.2307/1969558
[9] Massera, J. L.: Contributions to Stability Theory. Ann. of Math. (2) 64, 182–206 (1956). · Zbl 0070.31003 · doi:10.2307/1969955
[10] Persidskii, K. P.: On the Theory of Stability of Solutions of Differential Equations. Uspehi, Matem. Nauk (N.S.) 1, 250–255 (1946) [Russian].
[11] Stokes, A.: The Applications of a Fixed Point Theorem to a Variety of Nonlinear Stability Problems. Contributions to the theory of non-linear oscillations 5, pp. 173–184, Ann. of Math. Studies 45, Princeton Univ. Press, 1960. · Zbl 0104.06301
[12] Yoshizawa, T.: On the Stability of Solutions of a System of Differential Equations. Mem. Coll. Sci. Univ. Kyoto., Ser. A 29, 27–33 (1955). · Zbl 0064.34003
[13] Mikolajska, Z.: Sur la stabilité asymptotique des solutions d’un système d’équations différentielles. Ann. Polon. Math. 7, 13–19 (1959).
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