# On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Annales Polonici Mathematici (1995)

- Volume: 62, Issue: 3, page 283-291
- ISSN: 0066-2216

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topWenjie Gao, and Junyu Wang. "On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions." Annales Polonici Mathematici 62.3 (1995): 283-291. <http://eudml.org/doc/262667>.

@article{WenjieGao1995,

abstract = {The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].},

author = {Wenjie Gao, Junyu Wang},

journal = {Annales Polonici Mathematici},

keywords = {two-point boundary value problems; upper and lower solutions; Nagumo condition; existence; Carathéodory functions; second order periodic boundary value problem; Schauder fixed point theorem; minimal and maximal solutions; monotone iterative technique},

language = {eng},

number = {3},

pages = {283-291},

title = {On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions},

url = {http://eudml.org/doc/262667},

volume = {62},

year = {1995},

}

TY - JOUR

AU - Wenjie Gao

AU - Junyu Wang

TI - On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

JO - Annales Polonici Mathematici

PY - 1995

VL - 62

IS - 3

SP - 283

EP - 291

AB - The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].

LA - eng

KW - two-point boundary value problems; upper and lower solutions; Nagumo condition; existence; Carathéodory functions; second order periodic boundary value problem; Schauder fixed point theorem; minimal and maximal solutions; monotone iterative technique

UR - http://eudml.org/doc/262667

ER -

## References

top- [1] A. Adje, Sur et sous-solutions généralisées et problèmes aux limites du second ordre, Bull. Soc. Math. Belgique Sér. B 42 (1990), 347-368. Zbl0724.34018
- [2] J. Bebernes, A simple alternative problem for finding periodic solutions of second order ordinary differential systems, Proc. Amer. Math. Soc. 42 (1974), 121-127. Zbl0286.34055
- [3] 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
- [4] J. J. Nieto, Nonlinear second-order periodic boundary value problems with Carathéodory functions, Appl. Anal. 34 (1989), 111-128. Zbl0662.34022
- [5] M.-X. Wang, A. Cabada and J. J. Nieto, Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions, Ann. Polon. Math. 58 (1993), 221-235. Zbl0789.34027

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