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Asymptotic estimates for the solutions of boundary-value problems with initial jump for linear differential equations with small parameter in the coefficients of derivatives

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Ukrainian Mathematical Journal Aims and scope

We establish asymptotic estimates for the solutions of singularly perturbed boundary-value problems with initial jumps.

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References

  1. A. N. Tikhonov, “On the dependence of solutions of differential equations on a small parameter,” Mat. Sb., 22 (64), No. 2, 193–204 (1948).

    Google Scholar 

  2. M. I. Vishik and L. A. Lyusternik, “Regular degeneration and the boundary layer for linear differential equations with small parameter,” Usp. Mat. Nauk, 12, No. 5, 3–122 (1957).

    MathSciNet  MATH  Google Scholar 

  3. A. B. Vasil’eva, “Asymptotics of solutions of some boundary-value problems for quasilinear equations with small parameter at the higher derivative,” Dokl. Akad. Nauk SSSR, 123, No. 4, 583–586 (1958).

    MathSciNet  MATH  Google Scholar 

  4. N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  5. E. F. Mishchenko and N. Kh. Rozov, Differential Equations with Small Parameter and Relaxation Oscillations [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  6. M. I. Imanaliev, “Asymptotic methods in the theory of singularly perturbed integrodifferential systems,” in: Investigations of Integrodifferential Equations [in Russian], Ilim, Frunze, Vol. 2 (1962), pp. 21–39.

  7. S. A. Lomov, Introduction to the General Theory of Singular Perturbations [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  8. V. F. Butuzov, “Angular boundary layer in mixed singularly perturbed problems for hyperbolic equations of the second order,” Dokl. Akad. Nauk SSSR, 235, No. 5, 997–1000 (1977).

    MathSciNet  Google Scholar 

  9. M. I. Vishik and L. A. Lyusternik, “On the initial jump for nonlinear differential equations containing a small parameter,” Dokl. Akad. Nauk SSSR, 132, No. 6, 1242–1245 (1960).

    Google Scholar 

  10. K. A. Kasymov and D. N. Nurgabyl, “Asymptotic behavior of solutions of linear singularly perturbed general separated boundaryvalue problems with initial jump,” Ukr. Mat. Zh., 55, No. 11, 1496–1508 (2003); English translation: Ukr. Math. J., 55, No. 11, 1777–1792 (2003).

    Article  MathSciNet  Google Scholar 

  11. K. A. Kasymov and D. N. Nurgabyl, “Asymptotic estimates for the solutions of singularly perturbed boundary-value problems with initial jump for linear differential equations,” Differents. Uravn., 40, No. 4, 597–607 (2004).

    MathSciNet  Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 5, pp. 629–641, May, 2013.

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Kasymov, K.A., Nurgabyl, D.N. & Uaisov, A.B. Asymptotic estimates for the solutions of boundary-value problems with initial jump for linear differential equations with small parameter in the coefficients of derivatives. Ukr Math J 65, 694–708 (2013). https://doi.org/10.1007/s11253-013-0807-5

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  • DOI: https://doi.org/10.1007/s11253-013-0807-5

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