Autors: Karandjulov, L. I., Stoyanova, Y. P.
Title: Boundary Value Problem for Nonlinear Singularity perturbed Systems in Critical
Keywords: Boundary value problem, singularly perturbed nonlinear sysem

Abstract: A nonlinear singularly perturbed boundary - value problem is considered in the critical case of conditional stability. An asymptotic solution is constructed under certain assumptions and utilizing boundary functions and pseudoinverse of matrices and projectors.


  1. Boichuk, A. A., 1998, Nonlinear boundary value problem for system of ordinary differential equations, UMZ, Volume 50(2), pp. 162-171
  2. Cambell, S. L., 1987, A general form for solvable linear time varying singular systems of differential equations, SIAM J. Malh.Anal, Volume 18(4), pp. 1101-1115
  3. Coddington, E. A., Levinson N., 1958, Theory of ordinary differential equations, Moscow, IL
  4. Nashed, M.Z., 1976, Generalize Inverse and Applications, New York, San Francisco, London, Acad. Press
  5. Karandjulov, L. I., 1999, Conditional stable case for singularly perturbed Notherian boundary value problems, Nelinejni kolivaniya, Volume 2(2), pp. 194-208
  6. Karandjulov, L. I., Stoyanova, Ya. P., 2000, Boundary value problem for almost nonlinear singularly perturbed systems of ordinary differential equations, Serdica Math. J., Volume 26(4), pp. 309-330
  7. Kozlovskaya, T. D., 1973, Boundary value problem for conditional stable system with different small parameter at the higher derivative, Diferentz. uravneniya, Volume 9(5), pp. 832-84f5
  8. Penrose R., 1956, On best approxmate solution on linear matrix equations, Proc. Cambrige, Volume 52, pp. 17–19
  9. Penrose R., 1955, A generalize inverse for matrices, Proc. Cambrige Philos. Soc., Volume 51, pp. 406–413
  10. Samoilenko, A. M., Yakovetz, V. P., 1993, About transformation of linear systems into central canonical form, Dokl. Acad. Nauk Ukraine, Volume 4, pp. 10-15
  11. Samoilenko, A. M., Boichuk, A. A., Karandjulov, L. I.,, 2001, Noether boundary value problem with singular perturbation, Diferentz. uravneniya, Volume 37(9), pp. 1186-1103
  12. Vasil'eva, A. B., Butuzov, V. F., 1973, Asymptotic expansion of solution of singularly perturbed equations, Moscow, Nauka
  13. Vasil'eva, A. B., Butuzov, V. F., 1978, Singularly perturbed equations in the critical case, Moscow, Moscow State University
  14. Vasil'eva, A. B., Faminskaya, 1977, Boundary value problem for nonlinear singularly perturbed differential and delay systems when the non perturbed system is considered at the spectrum, Diferentz. uravneniya, Volume 13(4), pp. 738-742
  15. Zhoug M.G., Nefedov N.N., O’Mally R.E., 1989, On singular singularly perturbed initial, SIAM J. Appl. Math., Volume 49 (1), pp. 1–25


Bulletin of the Greek Mathematical Society, vol. 47, pp. 91-116, 2003, Greece, ISSN 0072-7466

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