Conditions for the existence of positive solutions covering a class of boundary value problems in a uniform way (Q417785)

The authors consider the class of second order differential equations NEWLINE\[NEWLINEx''(t)+f(t,x(t),x'(t))=0NEWLINE\]NEWLINE with the initial condition \(x(0)=0\) and a functional condition \(\alpha(x')=\xi\) for some functional \(\alpha\). Conditions on \(\alpha\) and on the function \(f\) are given such that Krasnosel'skii's fixed point theorem can be applied to provide the existence of positive solutions.