On nonresonance impulsive functional nonconvex valued differential inclusions

Mouffak Benchohra; Johnny Henderson; Sotiris K. Ntouyas

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 4, page 595-604
  • ISSN: 0010-2628

Abstract

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In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces.

How to cite

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Benchohra, Mouffak, Henderson, Johnny, and Ntouyas, Sotiris K.. "On nonresonance impulsive functional nonconvex valued differential inclusions." Commentationes Mathematicae Universitatis Carolinae 43.4 (2002): 595-604. <http://eudml.org/doc/248964>.

@article{Benchohra2002,
abstract = {In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces.},
author = {Benchohra, Mouffak, Henderson, Johnny, Ntouyas, Sotiris K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {impulsive functional differential inclusions; nonresonance problem; fixed point; Banach space; impulsive functional differential inclusions; nonresonance problems; fixed point; Banach space},
language = {eng},
number = {4},
pages = {595-604},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On nonresonance impulsive functional nonconvex valued differential inclusions},
url = {http://eudml.org/doc/248964},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Benchohra, Mouffak
AU - Henderson, Johnny
AU - Ntouyas, Sotiris K.
TI - On nonresonance impulsive functional nonconvex valued differential inclusions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 4
SP - 595
EP - 604
AB - In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces.
LA - eng
KW - impulsive functional differential inclusions; nonresonance problem; fixed point; Banach space; impulsive functional differential inclusions; nonresonance problems; fixed point; Banach space
UR - http://eudml.org/doc/248964
ER -

References

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  1. Bainov D.D., Simeonov P.S., Systems with Impulse Effect, Ellis Horwood Ltd., Chichister, 1989. Zbl0714.34083MR1010418
  2. Benchohra M., Eloe P., On nonresonance impulsive functional differential equations with periodic boundary conditions, Appl. Math. E.-Notes 1 (2001), 65-72. (2001) Zbl0983.34077MR1833839
  3. Benchohra MK., Henderson J., Ntouyas S.K., On nonresonance impulsive functional differential inclusions with periodic boundary conditions, Intern. J. Appl. Math. 5 (4) (2001), 377-391. (2001) Zbl1038.34083MR1852836
  4. Benchohra M., Henderson J., Ntouyas S.K., On nonresonance second order impulsive functional differential inclusions with nonlinear boundary conditions, Canad. Appl. Math. Quart., in press. Zbl1146.34055
  5. Castaing C., Valadier M., Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl0346.46038MR0467310
  6. Covitz H., Nadler S.B., Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11. (1970) MR0263062
  7. Deimling K., Multivalued Differential Equations, Walter de Gruyter, Berlin-New York, 1992. Zbl0820.34009MR1189795
  8. Dong Y., Periodic boundary value problems for functional differential equations with impulses, J. Math. Anal. Appl. 210 (1997), 170-181. (1997) Zbl0878.34059MR1449515
  9. Gorniewicz L., Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999. Zbl1107.55001MR1748378
  10. Hu Sh., Papageorgiou N., Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1997. Zbl0887.47001MR1485775
  11. Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. Zbl0719.34002MR1082551
  12. Nieto J.J., Basic theory for nonresonance impulsive periodic problems of first order, J. Math. Anal. Appl. 205 (1997), 423-433. (1997) Zbl0870.34009MR1428357
  13. Samoilenko A.M., Perestyuk N.A., Impulsive Differential Equations, World Scientific, Singapore, 1995. MR1355787

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