Focal subfunctions and second order differential inequalities
The authors are interested in the differential equation \(y''=f(x,y,y')\) associated with one of the following boundary conditions \(y(x_ 1)=y_ 1\), \(y'(x_ 2)=y_ 2\) and \(y(x_ 1)=y_ 1\), \(y(x_ 2)=y_ 2\), where \(x_ 1<x_ 2\) are reals. The main purpose is to provide sufficient conditions for the existence of solutions of those problems as well as to discuss when a given function is a so-called right focal subfunction with respect to such solutions.
scientific article; zbMATH DE number 150398