## 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 $$t\in \langle 0,T\rangle$$.

### MSC:

 45G05 Singular nonlinear integral equations 45M20 Positive solutions of integral equations
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### References:

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