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A monotone method for constructing extremal solutions to second-order periodic boundary value problems. (English) Zbl 0993.34011

Summary: The authors describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem \[ u''(t)= f(t,u,u'(t)),\quad t\in [0,2\pi],\quad u(0)= u(2\pi),\quad u'(0)= u'(2\pi), \] in the presence of an upper solution \(\beta\) and a lower solution \(\alpha\) with \(\beta\leq \alpha\).

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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