# Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Ming-Xing Wang; Alberto Cabada; Juan J. Nieto

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 3, page 221-235
- ISSN: 0066-2216

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topMing-Xing Wang, Alberto Cabada, and Juan J. Nieto. "Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions." Annales Polonici Mathematici 58.3 (1993): 221-235. <http://eudml.org/doc/262275>.

@article{Ming1993,

abstract = {The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.},

author = {Ming-Xing Wang, Alberto Cabada, Juan J. Nieto},

journal = {Annales Polonici Mathematici},

keywords = {upper and lower solutions; monotone iterative technique; Carathéodory function; periodic solutions; boundary value problem; generalized upper and lower solution method; minimal and maximal solutions},

language = {eng},

number = {3},

pages = {221-235},

title = {Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions},

url = {http://eudml.org/doc/262275},

volume = {58},

year = {1993},

}

TY - JOUR

AU - Ming-Xing Wang

AU - Alberto Cabada

AU - Juan J. Nieto

TI - Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 3

SP - 221

EP - 235

AB - The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.

LA - eng

KW - upper and lower solutions; monotone iterative technique; Carathéodory function; periodic solutions; boundary value problem; generalized upper and lower solution method; minimal and maximal solutions

UR - http://eudml.org/doc/262275

ER -

## References

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- [7] A. Cabada and J. J. Nieto, A generalization of the monotone iterative technique for nonlinear second-order periodic boundary value problems, J. Math. Anal. Appl. 151 (1990), 181-189. Zbl0719.34039
- [8] A. Cabada and J. J. Nieto, Extremal solutions of second-order nonlinear periodic boundary value problems, Appl. Math. Comput. 40 (1990), 135-145. Zbl0723.65056
- [9] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, New York, 1985. Zbl0658.35003
- [10] J. J. Nieto, Nonlinear second-order periodic boundary value problems with Carathé- odory functions, Applicable Anal. 34 (1989), 111-128.
- [11] D. R. Smart, Fixed Points Theorems, Cambridge University Press, Cambridge, 1974. Zbl0297.47042
- [12] M. X. Wang, Monotone method for nonlinear periodic boundary value problems, J. Beijing Inst. Technol. 9 (1989), 74-81 (in Chinese). Zbl0717.34021

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