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Existence and uniqueness of solutions for third-order nonlinear boundary value problems. (English) Zbl 1160.34312

Consider the boundary value problem \[ y'''f(x,y,y',y''),\;0<x<1, \]
\[ k(y(0),y'(0))=0,\;g(y'(0),y''(0))=0,\tag{*} \]
\[ h(y(0),y'(0),y''(0);\;y(1),y'(1),y''(1))=0, \] where \(k,g\) and \(h\) are continuous. The authors provide sufficient conditions for the existence and uniqueness of a solution to (*).

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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