Extremal solutions of second order nonlinear periodic boundary value problems
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 \(u'\).
scientific article; zbMATH DE number 4192984