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Third-order boundary value problems with sign-changing solutions. (English) Zbl 1130.34010
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.

##### MSC:
 34B15 Nonlinear boundary value problems for ODE
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##### References:
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