Some general existence principles for ordinary differential equations (Q1327685)

The authors establish some general existence principles for the first order initial value problem \(y'=f(t,y)\), \(0<t<T\), \(y(0)=a\) and the second order boundary value problem \((py')'=f(t,y,py')\), \(0<t<1\), \(-\alpha y(0) + \beta \lim_{t \to 0 + } p(t)y'(t) = c\) \(\alpha \geq 0\), \(\beta\geq 0\), \(ay(1) + b \lim_{t \to 1-} p(t)y'(t) = d\) \(a\geq 0\), \(b \geq 0\) and \(\alpha + a>0\). The results of the paper extend and complement the existing theory in the literature. In particular, \(f\) need not be continuous or even Carathéodory.