Positive solutions for a class of Volterra integral equations via a fixed point theorem in Fréchet spaces (Q854524)

The authors establish the existence of positive solutions to the Volterra integral equation \[ y(t)=\int_{0}^{t}k(t,s)f(y(s))\,ds,\quad \text{for}\;t\in [0,T), \] where \(0<T\leq\infty\). The proofs are based upon a fixed point theorem due to the authors which is an extension of the well-known Krasnoselskiĭ's fixed point theorem in cones to the Fréchet space setting. An application to the Emden differential equation \[ y''-t^{p}y^{q}=0, \] with \(p\geq 0\) and \(0<q<1\) is considered.