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.


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