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].
@article{bwmeta1.element.bwnjournal-article-apmv62z3p283bwm,
author = {Wenjie Gao and Junyu Wang},
title = {On a nonlinear second order periodic boundaryvalue problem with Carath\'eodory functions},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {283-291},
zbl = {0839.34031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv62z3p283bwm}
}
Wenjie Gao; Junyu Wang. On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions. Annales Polonici Mathematici, Tome 62 (1995) pp. 283-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv62z3p283bwm/
[000] [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. | Zbl 0724.34018
[001] [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. | Zbl 0286.34055
[002] [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. | Zbl 0719.34039
[003] [4] J. J. Nieto, Nonlinear second-order periodic boundary value problems with Carathéodory functions, Appl. Anal. 34 (1989), 111-128. | Zbl 0662.34022
[004] [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. | Zbl 0789.34027