The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations

Eduardo Liz; Juan J. Nieto

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 405-411
  • ISSN: 0010-2628

Abstract

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In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.

How to cite

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Liz, Eduardo, and Nieto, Juan J.. "The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 405-411. <http://eudml.org/doc/247515>.

@article{Liz1993,
abstract = {In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.},
author = {Liz, Eduardo, Nieto, Juan J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {impulsive differential equations; periodic boundary value problem; monotone iterative technique; monotone iterative technique; extremal solutions; second order periodic boundary value problem; impulsive effects; maximum principle},
language = {eng},
number = {3},
pages = {405-411},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations},
url = {http://eudml.org/doc/247515},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Liz, Eduardo
AU - Nieto, Juan J.
TI - The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 405
EP - 411
AB - In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.
LA - eng
KW - impulsive differential equations; periodic boundary value problem; monotone iterative technique; monotone iterative technique; extremal solutions; second order periodic boundary value problem; impulsive effects; maximum principle
UR - http://eudml.org/doc/247515
ER -

References

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  1. Cabada A., Nieto J.J., A generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems, J. Math. Anal. Appl. 151 (1990), 181-189. (1990) Zbl0719.34039MR1069454
  2. Hale J., Theory of functional differential equations, Springer-Verlag, New York, 1977. Zbl1092.34500MR0508721
  3. Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of impulsive differential equations, World Scientific, Singapore, 1989. Zbl0719.34002MR1082551
  4. Hu S., Lakshmikantham V., Periodic boundary value problems for second order impulsive differential systems, Nonlinear Anal. 13 (1989), 75-85. (1989) Zbl0712.34033MR0973370
  5. Ladde G.S., Lakshmikantham V., Vatsala A.S., Monotone iterative techniques for nonlinear differential equations, Pitman Advanced Publishing Program, 1985. Zbl0658.35003MR0855240
  6. Liu X., Nonlinear boundary value problems for first order impulsive integro-differential equations, Applicable Anal. 36 (1989), 119-130. (1989) Zbl0688.45015MR1040882
  7. Liz E., Nieto J.J., Periodic solutions of discontinuous impulsive differential systems, J. Math. Anal. Appl. 161 (1991), 388-394. (1991) Zbl0753.34027MR1132115
  8. Nieto J.J., Nonlinear second order periodic boundary value problems with Carathéodory functions, Applicable Anal. 34 (1989), 111-128. (1989) Zbl0662.34022MR0926825

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