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References
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).
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).
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).
J. D. Rauch and F. J. Vassey, “Differentiability of solutions to hyperbolic initial-boundary value problems,” Trans. Amer. Math. Soc,189, 303–318 (1974).
B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations [in Russian], Nauka, Moscow (1978).
S. K. Godunov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1979).
N. A. Eltysheva, “On qualitative properties of solutions to some hyperbolic systems on the plane,” Mat. Sb.,135, No. 2, 186–209 (1988).
N. A. Eltysheva, On Stability of Stationary Solutions to Some Problems for Hyperbolic Systems [in Russian], Dis. Kand. Fiz.-Mat. Nauk, Novosibirsk (1986).
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.)
M. Morse, “A generalization of Sturm separation and comparison theorems inn-space,” Math. Ann.,103, 52–93 (1930).
M. Morse, Variational Analysis: Critical Extremals and Sturmian Extensions, John Wiley and Sons, Inc., New York; London; Sydney; Toronto (1973).
T. I. Zelenyak, “On localization of eigenvalues of a certain spectral problem,” Sibirsk. Mat. Zh.,30, No. 2, 53–62 (1989).
Yu. L. Daletskii and M. G. Krein, Stability of Solutions to Differential Equations in Banach Space [in Russian], Nauka, Moscow (1970).
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.)
S. G. Pyatkov, “The Riesz basis property of proper and adjoint elements of linear selfadjoint pencils,” Mat. Sb.,185, No. 3, 93–116 (1994).
B. M. Levitan, Almost-Periodic Functions [in Russian], Gostekhizdat, Moscow (1953).
T. Kato, Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).
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The research is financially supported by the Russian Foundation for Basic Research (Grant 94-01-00878).
Translated fromSibirskii Matematicheskii Zhurnal, Vol. 37, No. 3, pp. 656–675, May–June, 1996.
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Skazka, V.V. On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. I. Solvability of the Lyapunov equation. Sib Math J 37, 573–590 (1996). https://doi.org/10.1007/BF02104860
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DOI: https://doi.org/10.1007/BF02104860