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On some three-point problems for third-order differential equations. (English) Zbl 0759.34020

The problem of the existence and uniqueness of solution of the three- point mixed problem \(u'''=f(t,u,u',u'')\), \(u(c)=0\), \(u'(a)=u'(b)\), \(u''(a)=u''(b)\), \(a\leq c\leq b\), is solved using the method of lower and upper solutions.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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