zbMATH — the first resource for mathematics

Implicit integral equations with discontinuous right-hand side. (English) Zbl 0886.47031
A theorem concerning the existence of a weak bounded solution on the half-line is proved for the integral equation $h(u(t)) = f (\int_I g(t,x)u(x)dx),$ where $$g:I\times I \rightarrow [0,\infty)$$, $$h:[\alpha,\beta]\rightarrow R$$ and $$f:[0,\sigma]\rightarrow R$$ $$(0<\alpha <\beta,\sigma >0)$$.
The main point is to overcome difficulties related to the discontinuity of the nonlinear function $$f$$. For this, the results for the associated inclusions of the type $\psi(u)(t) \in F(t,\phi(u)(t)),$ due to O. N. Ricceri and B. Ricceri [Appl. Anal. 38, No. 4, 259-270 (1990; Zbl 0706.47038)], have been employed.
Reviewer: J.Andres (Olomouc)

MSC:
 47H04 Set-valued operators
Zbl 0706.47038
Full Text: