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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

##### MSC:
 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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##### References:
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