Geodesic
The linearized uniform asymptotic stability of evolution differential equations
Czechoslovak Mathematical Journal, Tome 34 (1984) no. 2, pp. 257-284

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DOI : 10.21136/CMJ.1984.101949
Classification : 34G20, 35B35 
Neustupa, Jiří. The linearized uniform asymptotic stability of evolution differential equations. Czechoslovak Mathematical Journal, Tome 34 (1984) no. 2, pp. 257-284. doi: 10.21136/CMJ.1984.101949
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[1] Barták J.: Lyapunov Stability and Stability at Constantly Acting Disturbances of an Abstract Differential Equation of the Second Order. Czech. Math. Journal 26, 411 - 437, 1976. | MR

[2] Barták J.: Stability and Correctness of Abstract Differential Equations in Hilbert Spaces. Czech. Math. Journal 28, 548-593, 1978. | MR

[3] Barták J. J. Neustupa: A Note to Stability of the Equation of Oscillations of a Beam. (Russian). Čas. pro pěst. mat. 104, 338-352, 1979. | MR

[4] Daleckij J. L. M. G. Krejn: Stability of Solutions of Diflferential Equations in Banach Space. Moscow, Nauka 1970. (Russian) | MR

[5] Dunford N.. J. T. Schwartz: Linear Operators I. New York, John Wiley & Sons, Inc. 1958.

[6] Hahn W.: Stability of Motion. Berlin-Heidelberg-New York, Springer-Verlag 1967. | MR | Zbl

[7] Iooss G.: Theorie non linéaire de la stabilité des écoulements laminaires dans le cas de "l'échange des stabilités". Arch Rat. Mech. Anal. 40, 166-208, 1971. | DOI | MR | Zbl

[8] Iooss G.: Existence et stabilité de la solution périodique secondaire intervenant dans les problèmes d'évolution du type Navier-Stokes. Arch. Rat. Mech. Anal. 47, 301-329, 1972. | DOI | MR | Zbl

[9] Iooss G.: Bifurcation of a Periodic Solution of the Navier-Stokes Equations into an Invariant Torus. Arch. Rat. Mech. Anal. 58, 35-56, 1975. | DOI | MR | Zbl

[10] Kato T.: Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York, Springer-Verlag 1976. | MR | Zbl

[11] Kielhöfer H.: Stability and Semilinear Evolution Equations in Hubert Space. Arch. Rat. Mech. Anal. 57, 150-165, 1974. | DOI | MR

[12] Kielhöfer H.: On the Lyapunov Stability of Stationary Solutions of Semilinear Parabolic Differential Equations. Journal of Diff. Equations 22, 193-208, 1976. | DOI | MR

[13] Ladyzhenskaya O. A.: The Mathematical Theory of Viscous Incompressible Flow. Moscow, Nauka 1970. (Russian) | MR

[14] Ladyzhenskaya O. A. V. A. Solonnikov: On the Principle of Linearization and Invariant Manifolds for Problems of Magnetohydrodynamics. Zapisky naučnych seminarov LOMI, Vol. 38, Boundary-Value Problems of Math. Physics and Related Questions of the Function Theory 7, 46-93, Nauka 1973. (Russian) | MR

[15] Neustupa J.: The Uniform Exponential Stability and the Uniform Stability at Constantly Acting Disturbances of a Periodic Solution of the Wave Equation. Czech, Math. Journal 26, 388-410, 1976. | MR

[16] Neustupa J.: A Contribution to the Theory of Stability of Differential Equations in Banach Space. Czech. Math. Journal 29, 27-52, 1979. | MR | Zbl

[17] Neustupa J.: The Uniform Stability at Permanently Acting Disturbances of Evolution Differential Equations. To appear. | MR

[18] Prodi G.: Teoremi di tipo locale per il sistema di Navier-Stokes e stabilita del le soluzioni stazionarie. Rend. Sem. Mat. Univ. Padova 32, 374-397, 1962. | MR

[19] Sattinger D. H.: The Mathematical Problem of Hydrodynamic Stability. Journal of Math. and Mech. 18, 797-817, 1970. | MR | Zbl

[20] Sattinger D. H.: Topics in Stability and Bifurcation Theory. Lecture Notes in Mathematics, n. 309, Berlin-Heidelberg-New York, Springer-Verlag 1973. | MR | Zbl

[21] Solonnikov V. A.: Estimations of Solutions of the Nonstationary Navier-Stokes System. Zapisky naucnych seminarov LOMI, Vol. 38, Boundary-Value Problems of Math. Physics and Related Questions of the Function Theory 7, 153 - 231, Nauka 1973. (Russian) | MR

[22] Sova M.: Linear Differential Equations in Banach Spaces. Rozpravy ČSAV, Series of Math. and Natural Sciences, Vol. 85, No. 6, Academia Praha, 1975. | MR | Zbl

[23] Strauss A. J. A. Yorke: Perturbing Uniformly Asymptotically Stable Nonlinear Systems. Journal of Diff. Equations 6, 452-483, 1969. | DOI | MR

[24] Travis С. С. G. F. Webb: Existence and Stability for Partial Differential Equations. Transactions of the Amer. Math. Soc. 200, 395-418, 1974. | DOI | MR

[25] Yosida K.: Functional Analysis. Berlin-Heidelberg-New York, Springer-Verlag 1971. | Zbl

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