Third-order boundary value problems with sign-changing solutions (Q880288)

The authors are concerned with the existence of sign-changing solutions for a third order differential equation \[ u'''(t)=f(t,u(t),u'(t),u''(t)),\quad\text{ a.e. } t\in (0,1), \] subject to the boundary conditions \(u(0)=u'(0)=u''(1)=0\) or \(u(0)=u'(1)=u''(1)=0\). The proof of the main results are based on the Leray-Schauder continuation principle.