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Nonlinear second order periodic boundary value problems with Caratheodory functions. (English) Zbl 0662.34022
The authors consider the periodic boundary value problem \(-u''=f(t,u)\), \(u(0)=u(2\pi)\), \(u'(0)=u'(2\pi)\) when f satisfies Carathéodory conditions. It is shown that a generalized upper and lower solution method is still valid and develop monotone iterative technique for finding minimal and maximal solutions. Moreover, the authors prove that the set of solutions between the (generalized) lower and upper solutions is a compact and convex set provided that f is decreasing in u for fixed t.
Reviewer: J.J.Nieto

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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