A monotone method for constructing extremal solutions to second order periodic boundary value problems
Volume 76 / 2001
Annales Polonici Mathematici 76 (2001), 279-286
MSC: 34B10, 34B15.
DOI: 10.4064/ap76-3-6
Abstract
We describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem $u''(t)=f(t,u(t),u'(t))$, $u(0)=u(2\pi )$, $u'(0)=u'(2\pi )$ in the presence of a lower solution $\alpha (t)$ and an upper solution $\beta (t)$ with $\beta (t)\le \alpha (t)$.
