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Sell, G. R.

Boundedness of solutions of ordinary differential equations and Lyapunov functions. (English) Zbl 0131.08602

J. Math. Anal. Appl. 9, 477-490 (1964).
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Keywords:

ordinary differential equations
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References:

[1] Yoshizawa, T., Note on the boundedness of solutions of a system of differential equations, (Mem. Coll. Sci. Univ. Kyoto, Ser. A, 28 (1954)), 293-298 · Zbl 0056.31404
[2] Yoshizawa, T., Note on the boundedness and the ultimate boundedness of solutions of \(x′ = F(t, x)\), (Mem. Coll. Sci. Univ. Kyoto, Ser. A, 29 (1955)), 275-291 · Zbl 0067.31504
[3] Yoshizawa, T., Appendix to the paper “Note on the boundedness and the ultimate boundedness”, (Mem. Coll. Sci. Univ. Kyoto, Ser. A, 30 (1957)), 91-103 · Zbl 0079.30203
[4] Yoshizawa, T., On the necessary and sufficient condition for the uniform boundedness of solutions of \(x′ = F(t, x)\), (Mem. Coll. Sci. Univ. Kyoto, Ser. A, 30 (1957)), 217-226 · Zbl 0079.30301
[5] Yoshizawa, T., Liapunov’s function and boundedness of solutions, Funkcial. Ekvac., 2, 95-142 (1959) · Zbl 0093.28005
[6] Auslander, J., and Seibert, P.Ann. Inst. Fourier (Grenoble); Auslander, J., and Seibert, P.Ann. Inst. Fourier (Grenoble)
[7] Sell, G. R., Stability theory and Lyapunov’s second method, Arch. Rat. Mech. Anal., 14, 108-126 (1963) · Zbl 0133.34902
[8] Auslander, J.; Seibert, P., Prolongations and generalized Liapunov functions, (Intern. Symp. Nonlinear Diff. Eqs. and Nonlinear Mech. (1963), Academic Press), 454-462 · Zbl 0132.32204
[9] Ważewski, T., Une méthode topologique de l’examen du phénomène asymptotique relativement aux équations différentielles ordinaires, Rend. Accad. Lincei, 3, 210-215 (1947) · Zbl 0029.29302
[10] Malkin, I. G., Theory of Stability of Motion, AEC Translation No. 3352 (1952), Translation of publication of the state publishing house of technical-theoretical literature, Moscow-Leningrad · Zbl 0048.32801
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