Existence and uniqueness theorems for third order boundary value problems (Q1087684)

This paper deals with the existence and uniqueness conditions for third order differential equation of the type, \(y\prime''=f(x,y,y',y'')\) where \(f\in C[[0,1]\times R\times R\times R,R]\) under the following type of boundary conditions: \(y(0)=y_ 0\), \(y'(0)=\bar y_ 0\), \(y'(1)=y_ 1\). The equation (*) is transformed into a second order integro-differential equation, and then the known results for second order boundary value problems and Schauder's fixed point theorem are applied.