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Non-autonomous vector integral equations with discontinuous right-hand side. (English) Zbl 1055.45004
An existence of an $$L^s$$-solution, $$s\in \, ]1, \infty ]$$, is proved for the integral equation $u(t) = f\left(t, \int _I g(t,z)u(z)\,dz\right),$ where $$f$$ is not necessarily continuous in the second variable. The result is obtained by transforming the original problem to the one for a certain operator inclusion. Thus, another result of this type obtained earlier by the author jointly with F. Cammaroto in [Commentat. Math. Univ. Carolin. 40, 483–490 (1999; Zbl 1065.47505)] is generalized.

##### MSC:
 45G10 Other nonlinear integral equations
##### Keywords:
$$L^s$$-solutions; nonlinearities; operator inclusion
Zbl 1065.47505
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