Autors: Karandjulov, L. I., Stoyanova, Y. P.
Title: Generalized initial value problem for singularly perturbed impulsive systems
Keywords: generalized initial value problem, singular perturbation, as

Abstract: A generalized Cauchy problem for linear singularly perturbed systems with generalized impulse actions is considered. The asymptotic expansion is constructed by boundary functions utilizing generalized inverse matrices.


  1. D. D. B a i n o v, V. K o v a c h e v, 1994, Impulsive Differential Equations with a Small Parameter, Singapore, World Scientific Publishing Co. Ptc. Ltd.
  2. L. I. K a r a n d j u l o v, 1999, Generalized Cauchy problem for linear pulse differential systems. In: Mathematics and Education in Mathematics, Proc. of Twenty Eighth Spring Conference of the Union of Bulgarian Mathematicians, Montana, Bulgaria, 5-8 april 1999, <Sofia>, SBM
  3. L. I. K a r a n d j u l o v, Y. P. S t o y a n o v a, 2000, Generalized problem of Cauchy for definite class of singularly perturbed systems of ordinary differential equations with impulse effects. In: Applications of Mathematics in Engineering and Economics, Proc. of the XXV Summer School, Sozopol, Bulgaria, 1999, <Sofia>, Heron Press
  4. M. Z. N a s h e d, 1976, Generalized Inverse and Applications, New York-San Francisco-London, Acad. Press
  5. A. M. S a m o i l e n k o, N. A. P e r e s t y u k, 1995, Impulsive Differential Equations, Singapore, World Scientific Series on Nonlinear Science, Ser. A: Monographs and Treatises, 14, World Scientific
  6. R. P e n r o s e, 1955, A generalized inverse for matrices, Proc. Cambrige Philos. Soc, Volume 51, pp. 406-413
  7. A. B. V a s i l’e v a, V. F. B u t u z o v, 1973, Asymptotic Expansions of Solutions of Singularly Perturbed Equations,, Moscow, Nauka


Mathematica Balkanica, New Series, vol. 17, issue 1, pp. 133-146, 2003, Bulgaria, ISSN 0205-3217

Copyright Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

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