# 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

top- Aftabizadeh A.R., Gupta C.P., Xu J.M., Existence and uniqueness theorems for three-point boundary value problems, SIAM J. Math. Anal. 20 (1989), 716-726. (1989) Zbl0704.34019MR0990873
- Aftabizadeh A.R., Gupta C.P., Xu J.M., Periodic boundary value problems for third order ordinary differential equations, Nonlinear Anal. 14 (1990), 1-10. (1990) Zbl0706.34018MR1028242
- Afuwape A.U., Omari P., Zanolin F., Nonlinear perturbations of differential operators with nontrivial kernel and applications to third-order periodic boundary value problems, J. Math. Anal. Appl. 143 (1989), 35-56. (1989) Zbl0695.47044MR1019448
- Afuwape A.U., Zanolin F., An existence theorem for periodic solutions and applications to some third order nonlinear differential equations, preprint. Zbl0695.47044
- Agarwal R.P., Boundary Value Problems for Higher Order Differential Equations, World Scientific, Singapore, 1986. Zbl0921.34021MR1021979
- Agarwal R.P., Existence-uniqueness and iterative methods for third-order boundary value problems, J. Comp. Appl. Math. 17 (1987), 271-289. (1987) Zbl0617.34008MR0883170
- 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
- Ezeilo J.O.C., Nkashama M.N., Resonant and nonresonant oscillations for some third order nonlinear ordinary differential equations, Nonlinear Anal. 12 (1988), 1029-1046. (1988) Zbl0676.34021MR0962767
- Gregus M., Third Order Linear Differential Equations, D. Reidel, Dordrecht, 1987. Zbl0602.34005MR0882545
- Ladde G.S., Lakshmikantham V., Vatsala A.S., Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985. Zbl0658.35003MR0855240
- Lakshmikantham V., Nieto J.J., Sun Y., An existence result about periodic boundary value problems of second order differential equations, Appl. Anal., to appear. Zbl0691.34019MR1121320
- Nieto J.J., Nonlinear second order periodic boundary value problems, J. Math. Anal. Appl. 130 (1988), 22-29. (1988) Zbl0678.34022MR0926825
- 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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