Vector integral equations with discontinuous right-hand side. (English) Zbl 1065.47505

The authors consider the integral equation \[ u(t)=f\Big (\int ^1_0 g(t,z) u(z) dz\Big )\tag{1} \] where \(g\: [0,1] \times [0,1] \rightarrow [0, + \infty )\), \(f\: \mathbb{R}^n\rightarrow \mathbb{R}^n\) are given functions and \(f\) can be discontinuous. They extend an existence theorem for the equation (1) which was previously obtained by the authors in [Comment. Math. Univ. Carolin. 38, 241-246 (1997; Zbl 0886.47031)] for the case \(n=1\), applying a theorem on multivalued mappings of O.Naselli Ricceri and B.Ricceri [Appl. Anal. 38, 259-270 (1990; Zbl 0687.47044)].


47N20 Applications of operator theory to differential and integral equations
45G10 Other nonlinear integral equations
47J05 Equations involving nonlinear operators (general)
47H04 Set-valued operators
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