## Non-autonomous implicit integral equations with discontinuous right-hand side.(English)Zbl 1099.45004

The authors study the problem of existence of solutions to the implicit integral equation $h(u(t))=f(t,\int _I g(t,z)u(z)\,dz)$ for almost all $$t\in I=[0,1]$$, and where $$f\: I\times [0,\lambda ]\to \mathbb R$$, $$g\: I\times I\to [0,\infty )$$ and $$h\: (0,\infty )\to \mathbb R$$. F. Cammaroto and P. Cubiotti [Commentat. Math. Univ. Carol. 38, No. 2, 241–246 (1997; Zbl 0886.47031)] established an existence theorem for solutions $$u\in L^ {\infty }(I)$$ to a less general equation under assumptions on $$f$$ considerably weaker than continuity. In the paper under review the existence of solutions $$u\in L^ s(I)$$ is established, again without a-priori assuming that $$f$$ is continuous.

### MSC:

 45G10 Other nonlinear integral equations

Zbl 0886.47031
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