Existence and uniqueness theorems for a third-order three-point boundary value problem. (English) Zbl 0826.34017

The authors prove existence and uniqueness theorems for \(u'''= f(x, u, u', u'')- e(x)\), \(u(0)= A\), \(u(\eta)= B\), \(u(1)= C\), \(0< \eta< 1\), where \(f\) satisfies Carathéodory’s condition, \(e\in L^1[0, 1]\). The conditions are of inequality type, and the applied method is the Leray- Schauder continuation theorem.


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