Skip to main content
Log in

On the seminar on qualitative theory of differential equations at Moscow state university

  • Chronicle
  • Published:
Differential Equations Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. 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.

  2. 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.

    MathSciNet  Google Scholar 

References

  1. 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.

    MathSciNet  Google Scholar 

References

  1. Courant, R. and Hilbert, D., Metody matematicheskoi fiziki (Methods ofMathematical Physics), Moscow, 1951, Vol. 1.

  2. 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.

    Article  MathSciNet  MATH  Google Scholar 

References

  1. Kachalov, V.I., Holomorphic Regularization of Singularly Perturbed Problems, Vestnik Moskov. Energ. Inst., 2010, no. 6, pp. 54–62.

References

  1. 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.

    Google Scholar 

  2. 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.

    MathSciNet  MATH  Google Scholar 

  3. 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.

    MATH  Google Scholar 

  4. Sergeev, I.N., Complex Characteristic Exponents of Exponentially Separated Systems, Differ. Uravn., 2011, vol. 47, no. 6, pp. 900–901.

    Google Scholar 

  5. 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.

    MathSciNet  Google Scholar 

  6. Goritskii, A.Yu., Characteristic Frequencies of Linear Combinations of Sines, Differ. Uravn., 2008, vol. 44, no. 6, p. 860.

    Google Scholar 

References

  1. Sergeev, I.N., Definition of Complete Frequencies of Solutions of a Linear System, Differ. Uravn., 2009, vol. 45, no. 6, p. 908.

    Google Scholar 

  2. 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.

    Google Scholar 

References

  1. Bogdanov, Yu.S., On Asymptotically Equivalent Linear Differential Systems, Differ. Uravn., 1965, vol. 1, no. 6, pp. 707–716.

    MathSciNet  MATH  Google Scholar 

  2. Mazanik, S.A., On Asymptotically Equivalent Linear Differential Systems, Differ. Uravn., 1981, vol. 17, no. 5, pp. 923–926.

    MathSciNet  MATH  Google Scholar 

  3. 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.

    MathSciNet  Google Scholar 

References

  1. Millionshchikov, V.M., Problems on Stabilizational Indices, Differ. Uravn., 1993, vol. 29, no. 11, p. 2017.

    Google Scholar 

References

  1. Millionshchikov, V.M., On Typical Properties of Conditional Exponential Stability. VI, Differ. Uravn., 1984, vol. 20, no. 6, p. 980.

    MathSciNet  Google Scholar 

References

  1. Sergeev, I.N., Definition of Complete Frequencies of Solutions of a Linear Equation, Differ. Uravn., 2008, vol. 44, no. 11, pp. 1577.

    MathSciNet  Google Scholar 

  2. 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

  1. Swift, J. and Hohenberg, P.S., Hydrodynamic Fluctuations at the Convective Instability, Phys. Rev., 1977, vol. A15, no. 1, pp. 319–328.

    Google Scholar 

  2. Malozemova, D.V., Buffer Phenomenon in Swift-Hohenberg Generalized Equation, Model. i Analiz Inform. Sist., 2010, vol. 17, no. 1, pp. 83–92.

    Google Scholar 

References

  1. 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.

    MathSciNet  MATH  Google Scholar 

  2. 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.

    MathSciNet  Google Scholar 

References

  1. Izobov, N.A. and Prokhorova, R.A., Lineinye differentsial’nye sistemy Koppelya-Konti (Linear Differential Coppel-Conti Systems), Minsk, 2008.

References

  1. 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.

  2. 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

  1. 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

  1. 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.

  2. Plaksina, I.M., On a Certain Model Singular Problem, Vestn. Perm. Univ. Mat. Mekh. Inform., 2010, no. 1 (1), pp. 19–23.

References

  1. Millionshchikov, V.M., Structurally Stable Properties of Linear Systems of Differential Equations, Differ. Uravn., 1969, vol. 5, no. 10, pp. 1775–1784.

    MATH  Google Scholar 

  2. 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.

    MathSciNet  MATH  Google Scholar 

  3. 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.

    MathSciNet  MATH  Google Scholar 

References

  1. 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.

  2. Nuzhdova, T.E., Simultaneous Achievability of Central Exponents of Two-Dimensional Linear Systems, Differ. Uravn., 1972, vol. 8, no. 8, pp. 1416–1422.

    Google Scholar 

  3. 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.

    MATH  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266111110152

Keywords

Navigation