Positive solutions of singular integral equations. (English) Zbl 0988.45004

The nonlinear singular integral equation \[ y(t)= h(t)+ \int^T_0 K(t,s)f \bigl(y(s)\bigr)ds,\;t\in\langle 0,T\rangle,\;T\in(0,+ \infty \rangle \] 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 \(t\in \langle 0,T\rangle\).


45G05 Singular nonlinear integral equations
45M20 Positive solutions of integral equations
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