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Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions. (English) Zbl 0789.34027

The authors investigate the existence of periodic solutions of the boundary value problem \(-u''(t)=f(t,u(t), u'(t))\), \(u(0)-u(2\pi) =u'(0)- u'(2\pi)=0\) when \(f\) satisfies the Carathéodory conditions. They combine the generalized upper and lower solution method and the monotone iterative technique to find minimal and maximal solutions.

MSC:

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