Siberian Mathematical Journal

, Volume 37, Issue 3, pp 573–590 | Cite as

On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. I. Solvability of the Lyapunov equation

  • V. V. Skazka


Hyperbolic System Spectral Problem Lyapunov Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. è. Abolinya and A. D. Myshkis, “On a mixed problem for a linear hyperbolic system on the plane,” Uchen. Zap. Latv. Univ.,20, 87–104 (1958).Google Scholar
  2. 2.
    K. V. Brushlinskii, “On growth of a solution to a mixed problem in the case when the system of eigenfunctions is incomplete,” Izv. Akad. Nauk SSSR Ser. Mat.,23, No. 6, 893–912 (1959).Google Scholar
  3. 3.
    V. è. Abolinya and A. D. Myshkis, “A mixed problem of an almost linear hyperbolic system on the plane,” Mat. Sb.,50, No. 4, 423–442 (1960).Google Scholar
  4. 4.
    J. D. Rauch and F. J. Vassey, “Differentiability of solutions to hyperbolic initial-boundary value problems,” Trans. Amer. Math. Soc,189, 303–318 (1974).Google Scholar
  5. 5.
    B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations [in Russian], Nauka, Moscow (1978).Google Scholar
  6. 6.
    S. K. Godunov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1979).Google Scholar
  7. 7.
    N. A. Eltysheva, “On qualitative properties of solutions to some hyperbolic systems on the plane,” Mat. Sb.,135, No. 2, 186–209 (1988).Google Scholar
  8. 8.
    N. A. Eltysheva, On Stability of Stationary Solutions to Some Problems for Hyperbolic Systems [in Russian], Dis. Kand. Fiz.-Mat. Nauk, Novosibirsk (1986).Google Scholar
  9. 9.
    V. S. Belonosov, “On instability indices of unbounded operators. I,” in: Some Applications of Functional Analysis to Equations of Mathematical Physics [in Russian], Novosibirsk, 1984, No. 2, pp. 25–51. (Trudy Seminara S. L. Soboleva.)Google Scholar
  10. 10.
    M. Morse, “A generalization of Sturm separation and comparison theorems inn-space,” Math. Ann.,103, 52–93 (1930).CrossRefMathSciNetGoogle Scholar
  11. 11.
    M. Morse, Variational Analysis: Critical Extremals and Sturmian Extensions, John Wiley and Sons, Inc., New York; London; Sydney; Toronto (1973).Google Scholar
  12. 12.
    T. I. Zelenyak, “On localization of eigenvalues of a certain spectral problem,” Sibirsk. Mat. Zh.,30, No. 2, 53–62 (1989).Google Scholar
  13. 13.
    Yu. L. Daletskii and M. G. Krein, Stability of Solutions to Differential Equations in Banach Space [in Russian], Nauka, Moscow (1970).Google Scholar
  14. 14.
    P. Grisvard, “An approach to the singular solutions of elliptic problems via the theory of differential equations in Banach spaces,” in: Differential Equations in Banach Spaces, Proc. Conf. Bologna, 1985, Springer, Berlin etc., 1986, pp. 131–156. (Lecture Notes in Math., 1223.)Google Scholar
  15. 15.
    S. G. Pyatkov, “The Riesz basis property of proper and adjoint elements of linear selfadjoint pencils,” Mat. Sb.,185, No. 3, 93–116 (1994).Google Scholar
  16. 16.
    B. M. Levitan, Almost-Periodic Functions [in Russian], Gostekhizdat, Moscow (1953).Google Scholar
  17. 17.
    T. Kato, Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. V. Skazka
    • 1
  1. 1.Novosibirsk

Personalised recommendations