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Existence and uniqueness theorems for third order boundary value problems. (English) Zbl 0611.34005
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.
Reviewer: S.L.Kalla

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34B99 Boundary value problems for ordinary differential equations
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