Minimal solutions for two point boundary value problems (Q912261)

This paper deals with a two point BVP \(y''-f(x,y,y')=0\), \(x\in <a,b>\), \(y(a)=A\), \(y(b)=B\), where f satisfies the Carathéodory conditions and \(y'\) is absolutely continuous on \(<a,b>\). The author proves that this problem with \((x,y(x),y'(x))\) in a specified region of \(<a,b>\times R^ 2\) (f satisfies certain differential inequalities) has a maximal and a minimal solution in this region.