Existence and uniqueness of solutions for third-order nonlinear boundary value problems (Q860546)

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 (*).