APPLICATION OF THE METHOD OF THE TWO-SIDED APPROXIMATIONS TO THE SOLUTION OF THE PERIODIC PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS

Authors

  • P. S. SIMEONOV Plovdiv University, "Paissii Hilendai-ski".
  • D. D. BAINOV Plovdiv University, "Paissii Hilendai-ski".

DOI:

https://doi.org/10.5556/j.tkjm.22.1991.4612

Keywords:

differential equations with impulses, periodic solutions

Abstract

In the paper the application of the method of the two-sided approximations to finding the periodic solutions of impulsive differential equations is justified.

References

Simeonov P. S., Bainov D. D., "Stability in linear approximation of systems with impulse effect", Rend. Sem. Mat. Univers. Politecn. Torino, Vol. 43°, 2, 303-322, 1985.

Simeonov P. S., Bainov D. D., "Stability with respect to part of the variables in systems with impulse effect", J. Math. Anal. Appl., Vol. 117, No. 1, 247-263, 1986.

Simeonov P. S., Bainov D. D., "Stability of the solutions of singularly perturbed systems with impulse effect", J. Math. Anal. Appl., Vol. 136, No. 2, 575-588, 1988.

Simeonov P. S., Bainov D. D., "Perturbation theorems for systems with impulse effect", Int. J. Systems Sci., Vol. 19, No. 7, 1213-1223, 1988.

Simeonov P. S., Bainov D. D., "On the asymptotic equivalence of systems with impulse effect", J. Math. Anal. Appl., Vol. 135, No. 2, 591-610, 1988.

Lakshmikantham V., Bainov D. D., Simeonov P. S., "Theory of Impulsive Differential Systems", World Scientific Publishing Co. Pte. Ltd, Singapore-New Jersey-London-Hong Kong.

Bainov D. D., Hu Shouchuan, Hristova S. G., Lakshmikantham V., "Periodic boundary value problems for systems of first order impulsive differential equations", J. Diff. and Integral Equations (to appear).

Lakshmikantham V., Liu Xinzhi., "Stability criteria for impulsive differential equations in terms of two measures", J. Math. Anal. Appl., Vol. 135, 591-604, 1989.

Hu Shouchuan, Lakshmikantham V., Leela S., "Impulsive differential equations and the pulse phenomena", J. Math. Anal. Appl., Vol. 137, 605-612, 1989.

Lakshmikantham V., Liu Xinzhi., "On quasi stability for impulsive differential systems", Nonlinear Analysis (to appear).

Mitropol'skii Yu. A., Martynyuk D. I., "Periodic and quasiperiodic oscillations of systems with delay", "Visca Skola", Kiev, 1979. (in Russian).

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Published

1991-09-01

How to Cite

SIMEONOV , P. S., & BAINOV, D. D. (1991). APPLICATION OF THE METHOD OF THE TWO-SIDED APPROXIMATIONS TO THE SOLUTION OF THE PERIODIC PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS. Tamkang Journal of Mathematics, 22(3), 275–284. https://doi.org/10.5556/j.tkjm.22.1991.4612

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Papers