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

Commentationes Mathematicae Universitatis Carolinae (1993)

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

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topLiz, 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

top- 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
- Hale J., Theory of functional differential equations, Springer-Verlag, New York, 1977. Zbl1092.34500MR0508721
- Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory of impulsive differential equations, World Scientific, Singapore, 1989. Zbl0719.34002MR1082551
- Hu S., Lakshmikantham V., Periodic boundary value problems for second order impulsive differential systems, Nonlinear Anal. 13 (1989), 75-85. (1989) Zbl0712.34033MR0973370
- Ladde G.S., Lakshmikantham V., Vatsala A.S., Monotone iterative techniques for nonlinear differential equations, Pitman Advanced Publishing Program, 1985. Zbl0658.35003MR0855240
- Liu X., Nonlinear boundary value problems for first order impulsive integro-differential equations, Applicable Anal. 36 (1989), 119-130. (1989) Zbl0688.45015MR1040882
- Liz E., Nieto J.J., Periodic solutions of discontinuous impulsive differential systems, J. Math. Anal. Appl. 161 (1991), 388-394. (1991) Zbl0753.34027MR1132115
- 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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