Extremal solutions of second order nonlinear periodic boundary value problems. (English) Zbl 0723.65056

The authors consider the periodic boundary value problems of the form \(- u''(t)=f(t,u(t),u'(t)),\text{ for } a.e.\quad t\in [0,2\pi],\quad u(0)=u(2\pi),\) where f is a Carathéodory function. They develop a monotone method to obtain the existence of extremal solutions between the lower and upper solutions as uniform limit of monotone sequences. This result is a generalization of results earlier obtained by the second author to the case of functions f depending also on \(u'\).


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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