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Keywords:
existence; uniqueness; three-point mixed problem; method of lower and upper solutions; lower and upper solutions; resonance; Carathéodory conditions
existence; uniqueness; three-point mixed problem; method of lower and upper solutions; lower and upper solutions; resonance; Carathéodory conditions
Summary:
This paper is concerned with existence and uniqueness of solutions of the three-point problem $u'''=f(t,u,u',u''), u(c)=0,u'(a)=u'(b). u''(a)=u''(b), a\leq c\leq b$. The problem is at resonance, in the sense that the associated linear problem has non-trivial solutions. We use the method of lower and upper solutions.
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