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Systems with small nonsymmetric matrix at the derivative

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We consider systems of differential equations with small, generally nonsymmetric matrix at the derivative. We study convergence inL 2 of solutions of these systems. In particular we prove theorems on convergence to a solution of the limit degenerate system.

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Literature cited

  1. V. P. Skripnik, “Convergence in L2 of solutions of systems with small matrix at the derivative,” Différents. Uravn.,24, No. 2, 357–359 (1988).

    Google Scholar 

  2. V. P. Skripnik, “Nonlinear systems with small matrix at the derivative in L2,” Izv. Izv. Vuzov. Matemat., No. 10, 34–39 (1989).

    Google Scholar 

  3. V. P. Skripnik, “Convergence in L2 of solutions of equations with small matrix at the derivative,” Ukr. Mat. Zh.,41, No. 6, 773–778 (1989).

    Google Scholar 

  4. A. B. Vasil'eva and M. G. Dmitriev, “Singular perturbations in problems of optimal control,” Itogi Nauki Tekhn., Ser. Mat. Analiz,20, 3–77 (1982).

    Google Scholar 

  5. A. N. Tikhonov, “Systems containing small parameters of the highest derivatives,” Mat. Sb.,31, No. 3, 575–586 (1952).

    Google Scholar 

  6. A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions of Solutions of Singularity Perturbed Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  7. E. F. Mishchenko and N. Kh. Rozov, Differential Equations with Small Parameter and Relaxational Oscillations [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  8. S. G. Krein and K. I. Chernyshov, “Behavior of solutions of general linear systems depending meromorphically on a small parameter,” Dokl. Akad. Nauk SSSR,260, No. 3, 530–535 (1982).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1528–1535, November, 1990.

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Skripnik, V.P. Systems with small nonsymmetric matrix at the derivative. Ukr Math J 42, 1370–1377 (1990). https://doi.org/10.1007/BF01066194

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  • DOI: https://doi.org/10.1007/BF01066194

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