Positive solutions of singular integral equations (Q5939763)

The nonlinear singular integral equation NEWLINE\[NEWLINEy(t)= h(t)+ \int^T_0 K(t,s)f \bigl(y(s)\bigr)ds,\;t\in\langle 0,T\rangle,\;T\in(0,+ \infty \rangleNEWLINE\]NEWLINE is considered. The Schauder fixed point theorem \((T< \infty)\) and the Schauder-Tikhonov fixed point theorem \((T=+ \infty)\) are used to establish the existence of continuous, positive solution of the equation with \(0<K(t,s)\in L^1 (0,T)\) for each \(t\in \langle 0,T\rangle\).