# Periodic solutions for third order ordinary differential equations

Commentationes Mathematicae Universitatis Carolinae (1991)

- Volume: 32, Issue: 3, page 495-499
- ISSN: 0010-2628

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topNieto, Juan J.. "Periodic solutions for third order ordinary differential equations." Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 495-499. <http://eudml.org/doc/21795>.

@article{Nieto1991,

abstract = {In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself.},

author = {Nieto, Juan J.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {periodic solution; maximum principle; upper and lower solutions; monotone method; periodic solutions; periodic boundary value problem; third-order ordinary differential equation; uniqueness},

language = {eng},

number = {3},

pages = {495-499},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Periodic solutions for third order ordinary differential equations},

url = {http://eudml.org/doc/21795},

volume = {32},

year = {1991},

}

TY - JOUR

AU - Nieto, Juan J.

TI - Periodic solutions for third order ordinary differential equations

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1991

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 32

IS - 3

SP - 495

EP - 499

AB - In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself.

LA - eng

KW - periodic solution; maximum principle; upper and lower solutions; monotone method; periodic solutions; periodic boundary value problem; third-order ordinary differential equation; uniqueness

UR - http://eudml.org/doc/21795

ER -

## References

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- Lakshmikantham V., Nieto J.J., Sun Y., An existence result about periodic boundary value problems of second order differential equations, Appl. Anal., to appear. MR1121320
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- Rudolf B., Kubacek Z., Remarks on J. J. Nieto's paper: Nonlinear second order periodic boundary value problems, J. Math. Anal. Appl. 146 (1990), 203-206. (1990) Zbl0713.34015MR1041210
- Temam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1988. Zbl0871.35001MR0953967

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