Geodesic
Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions
Annales Polonici Mathematici, Tome 58 (1993) no. 3, pp. 221-235.

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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.
DOI : 10.4064/ap-58-3-221-235
Keywords: upper and lower solutions, monotone iterative technique, Carathéodory function

Ming-Xing Wang 1 ; Alberto Cabada 1 ; Juan Nieto 1

1 
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Ming-Xing Wang; Alberto Cabada; Juan Nieto. Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions. Annales Polonici Mathematici, Tome 58 (1993) no. 3, pp. 221-235. doi : 10.4064/ap-58-3-221-235. http://geodesic.mathdoc.fr/articles/10.4064/ap-58-3-221-235/

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