×

On second order periodic boundary-value problems with upper and lower solutions in the reversed order. (English) Zbl 1096.34010

Summary: We study the differential equation with the periodic boundary value \[ u''(t)=f(t, u(t), u'(t)),\quad t\in [0, 2\pi],\quad u(0)=u(2\pi), \quad u'(0)=u'(2\pi). \] The existence of solutions to the periodic boundary problem with appropriate conditions is proved by using an upper and lower solution method.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: EuDML EMIS