Posts by Radu Precup

Abstract

We develop continuation technique to obtain periodic solutions for superlinear planar differential systems of first order with impulses.

Our approach was inspired by some works by Capietto, Mawhin and Zanolin in analogous problems without impulses and uses instead of Brouwer degree the much more elementary notion of essential map in the sense of fixed point theory.

Authors

Eduard Kirr
Faculty of Mathematics, University “Babes-Bolyai”

Radu Precup
Faculty of Mathematics, University “Babes-Bolyai”

Keywords

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Paper coordinates

E. Kirr, R. Precup, Periodic solutions of superlinear impulsive differential systems, Commun. Appl. Anal., 3  (1999), 483-502.

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About this paper

Journal

Communications in Applied Analysis

 

Publisher Name

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paper on the journal website
Print ISSN

Not available yet.

Online ISSN

1083-2564

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References

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2. Bainov, D. D., Kostadinov, S. I., & Zabreiko, P. P., Monotonic impulsive differential equations. Indian J. Pure Appl. Math., Vol 26 (1995) pp. 315-320.
3. Bainov, D. D., & Simeonov, P. S., Theory of impulsive differential equations: periodic solutions and applications. Longman, Harlow, 1993.
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5. Capietto, A., Mawhin, J., & Zanolin, F., Boundary value problems for forced superlinear second order ordinary differential equations. in Nonlinear Partial Differential Equations and their Applications, College de France Seminar, Vol 12 (Edited by H. Brezis and J.L. Lions) pp. 55-64, Longman, Harlow, 1994.
6. Dugundji, J., & Granas, A., Fixed point theory I. Polish Scientific Publishers, Warsaw, 1982.
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8. Gaines, R. E., & Mawhin, J., Coincidence degree and nonlinear differential equations. Lecture Notes in Math., Vol. 568, Springer-Verlag, Berlin, 1977.
9. Hristova, S. G., & Bainov, D. D., Existence of periodic solutions of nonlinear systems of differential equations with impulse effect. J. Math. Anal. Appl., Vol 125 (1987) pp. 192-202.
10. Hristova, S. G., & Bainov, D. D., Monotone-iterative techniques of V. Lakshmikantham for a boundary value problem for systems of impulsive differential-difference equations. J. Math. Anal. Appl., Vol 197 (1996) pp. 1-13.
11. Hu, S., & Lakshmikantham, V., Periodic boundary value problems for second order impulsive differential systems. Nonlinear Analysis, Vol 13 (1989) pp. 75-85.
12. Kirr, E., Periodic solutions for perturbed Hamiltonian systems with superlinear growth and impulsive effects. Studia Univ. Babes-Bolyai (Mathematica), Vol 41, No 4 (1996) in print.
13. Krasnoselskii, M. A., Perov, A. I., Povolotskii, A. I., & Zabreiko, P. P., Plane vector fields. Academic Press, New York, 1966.
14. Lakshmikantham, V., Bainov, D. D., & Simeonov, P. S., Theory of impulsive differential equations. World Scientific Pub., Singapore, 1989.
15. Li, Z. W., Periodic boundary value problems for second order impulsive integrodifferential equations of mixed type in Banach spaces. J. Math. Anal. Appl., Vol 195 (1995) pp. 214-229.
16. Liz, E., & Nieto, J. J., Periodic solutions of discontinuous impulsive differential systems. J. Math. Anal. Appl., Vol 161 (1991) pp. 388-394.
17. Liz, E., & Nieto, J. J., The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations. Comment. Math. Univ. Carolin., Vol 34 (1993) pp. 405-411.
18. Precup, R., A Granas type approach to some continuation theorems and periodic boundary value problems with impulses. Topological Methods in Nonlinear Analysis, Vol 5 (1995) pp. 385-396.
19. Precup, R., Continuation principles for coincidences. Mathematica (Cluj)., Vol 39(62) (1997) in print.

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