Existence of solutions for a two point boundary value problem (Q1086405)

We consider the two point boundary value problem \(F[y]=y''-f(x,y,y')=0\), \(a\leq x\leq b\), \(y(a)=A\), \(y(b)=B\). Assuming that f satisfies certain differential inequalities associated with the existence of F-subfunctions and F-superfunctions, and that f also satisfies a suitable growth condition with respect to y', we prove that the two point boundary value problem has a solution y with (x,y(x),y'(x)) in a specified region; indeed we show that the problem has a maximal and a minimal solution in this region. Our results unify and generalize earlier results of K. Ako, L. K. Jackson, M. Nagumo, and others.