References
Constantine, P., Foias, C., Nicolaenko, B., and Temam, R., Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations, Appl. Math. Sci., no. 70, New York, 1989.
Goritskii, A.Yu. and Chepyzhov, V.V., The Dichotomy Property of Solutions of Quasilinear Equations in Problems on Inertial Manifolds, Mat. Sb., 2005, vol. 196, no. 4, pp. 23–50.
References
Sergeev, I.N., The Determination and Properties of Characteristic Frequencies of Linear Equations, Tr. Semin. im. I.G. Petrovskogo, 2006, vol. 25, pp. 249–294.
References
Courant, R. and Hilbert, D., Metody matematicheskoi fiziki (Methods ofMathematical Physics), Moscow, 1951, Vol. 1.
Sperb, R., Untere und obere Schranken für den tiefsten Eigenwert elastisch gestützten Membran, Z. Angew. Math. Phys., 1972, vol. 23, no. 2, pp. 231–244.
References
Kachalov, V.I., Holomorphic Regularization of Singularly Perturbed Problems, Vestnik Moskov. Energ. Inst., 2010, no. 6, pp. 54–62.
References
Bylov, B.F., Vinograd, R.E., Grobman, D.M., and Nemytskii, V.V., Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti (Theory of Lyapunov Exponents and Its Application to Problems of Stability), Moscow: Nauka, 1966.
Izobov, N.A., The Measure of the Solution Set of a Linear System with the Largest Lower Exponent, Differ. Uravn., 1988, vol. 24, no. 12, pp. 2168–2170.
Millionshchikov, V.M., Systems with Integral Separation Are Dense Everywhere in the Set of All Linear Systems of Differential Equations, Differ. Uravn., 1969, vol. 5, no. 7, pp. 1167–1170.
Sergeev, I.N., Complex Characteristic Exponents of Exponentially Separated Systems, Differ. Uravn., 2011, vol. 47, no. 6, pp. 900–901.
Sergeev, I.N., Oscillation and Wandering of Solutions of Linear Differential Equations of Small Order, Differ. Uravn., 2011, vol. 47, no. 6, pp. 906–907.
Goritskii, A.Yu., Characteristic Frequencies of Linear Combinations of Sines, Differ. Uravn., 2008, vol. 44, no. 6, p. 860.
References
Sergeev, I.N., Definition of Complete Frequencies of Solutions of a Linear System, Differ. Uravn., 2009, vol. 45, no. 6, p. 908.
Sergeev, I.N., Comparison of Complete Frequencies and Wandering Exponents of Solutions of a Linear System, Differ. Uravn., 2010, vol. 46, no. 11, pp. 1667–1668.
References
Bogdanov, Yu.S., On Asymptotically Equivalent Linear Differential Systems, Differ. Uravn., 1965, vol. 1, no. 6, pp. 707–716.
Mazanik, S.A., On Asymptotically Equivalent Linear Differential Systems, Differ. Uravn., 1981, vol. 17, no. 5, pp. 923–926.
Izobov, N.A. and Mazanik, S.A., On Asymptotically Equivalent Linear Systems under Exponentially Decreasing Perturbations, Differ. Uravn., 2006, vol. 42, no. 2, pp. 168–173.
References
Millionshchikov, V.M., Problems on Stabilizational Indices, Differ. Uravn., 1993, vol. 29, no. 11, p. 2017.
References
Millionshchikov, V.M., On Typical Properties of Conditional Exponential Stability. VI, Differ. Uravn., 1984, vol. 20, no. 6, p. 980.
References
Sergeev, I.N., Definition of Complete Frequencies of Solutions of a Linear Equation, Differ. Uravn., 2008, vol. 44, no. 11, pp. 1577.
Sergeev, I.N., On the Control of Solutions of a Linear Differential Equation, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 2009, no. 3, pp. 25–33.
References
Swift, J. and Hohenberg, P.S., Hydrodynamic Fluctuations at the Convective Instability, Phys. Rev., 1977, vol. A15, no. 1, pp. 319–328.
Malozemova, D.V., Buffer Phenomenon in Swift-Hohenberg Generalized Equation, Model. i Analiz Inform. Sist., 2010, vol. 17, no. 1, pp. 83–92.
References
Krein, M.G. and Rutman, M.A., Linear Operators Leaving Invariant a Cone in a Banach Space, Uspekhi Mat. Nauk, 1948, vol. 3, no. 1, pp. 3–95.
Pankratova, I.N., On Invariant Sets of a Dynamical System by the Product of a Scalar Function and a Linear Vector Function, Differ. Uravn., 2009, vol. 45, no. 1, pp. 138–144.
References
Izobov, N.A. and Prokhorova, R.A., Lineinye differentsial’nye sistemy Koppelya-Konti (Linear Differential Coppel-Conti Systems), Minsk, 2008.
References
Zavgorodnii, M.G., Variational Principles in the Constructions of Models of Rod Systems, in Sb. nauchn. tr. “Matematicheskoe modelirovanie informatsionnykh i tekhnologicheskikh sistem” (Collection of Scientific Papers “Mathematical Modeling of Informational and Technological Systems”), Voronezh, 2000, no. 4, pp. 59–62.
Pokornyi, Yu.V., Penkin, O.M., Pryadiev, V.L., et al., Differentsial’nye uravneniya na geometricheskikh grafakh (Differential Equations on Geometric Graphs), Moscow, 2004.
References
Meshkov, V.Z. and Polovinkin, I.P., A Remark on Properties of Solutions of Linear Partial Differential Equations, Chernozem. Al’manakh Nauchn. Issled. Fundam. Mat., 2007, no. 1 (5), pp. 3–11.
References
Azbelev, N.V., Maksimov, V.P., and Rakhmatullina, L.F., Elementy sovremennoi teorii funktsional’nodifferentsial’nykh uravnenii. Metody i prilozheniya (Elements of the Modern Theory of Functional-Differential Equations. Methods and Applications), Moscow, 2002.
Plaksina, I.M., On a Certain Model Singular Problem, Vestn. Perm. Univ. Mat. Mekh. Inform., 2010, no. 1 (1), pp. 19–23.
References
Millionshchikov, V.M., Structurally Stable Properties of Linear Systems of Differential Equations, Differ. Uravn., 1969, vol. 5, no. 10, pp. 1775–1784.
Bylov, B.F. and Izobov, N.A., Necessary and Sufficient Conditions for the Stability of the Characteristic Exponents of a Linear System, Differ. Uravn., 1969, vol. 5, no. 10, pp. 1794–1803.
Sergeev, I.N., On the Theory of Lyapunov Exponents of Linear Systems of Differential Equations, Tr. Semin. im. I.G. Petrvoskogo, 1983, vol. 9, pp. 111–166.
References
Sergeev, I.N., On Perron Lower Characteristic Exponents of Linear Systems, in Mezhdunar. konf., posv. 103-letiyu so dnya rozhdeniya I.G. Petrovskogo: Tez. dokl. (Abstr. Int. Conf. Devoted to the 103rd Birthday of I.G. Petrovskii), Moscow, 2004, pp. 199–200.
Nuzhdova, T.E., Simultaneous Achievability of Central Exponents of Two-Dimensional Linear Systems, Differ. Uravn., 1972, vol. 8, no. 8, pp. 1416–1422.
Millionshchikov, V.M., Systems with Integral Separation Are Dense Everywhere in the Set of All Linear Systems of Differential Equations, Differ. Uravn., 1969, vol. 5, no. 7, pp. 1167–1170.
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On the seminar on qualitative theory of differential equations at Moscow state university. Diff Equat 47, 1680–1696 (2011). https://doi.org/10.1134/S0012266111110152
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DOI: https://doi.org/10.1134/S0012266111110152