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Perturbation of a single-valued operator by a multi-valued mapping of Hammerstein type with nonconvex images. (English. Russian original) Zbl 0999.47035
Russ. Math. 43, No. 3, 1-13 (1999); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1999, No. 3, 3-16 (1999).
The authors study the inclusion \(x\in f(x)+ V\Phi(x)\), where \(f: C([a,b],\mathbb{R}^n)\to C([a,b],\mathbb{R}^n)\) is compact, \(\Phi: C([a,b],\mathbb{R}^n)\to L^1([a,b],\mathbb{R}^n)\) is multivalued with certain additional properties, and \(V: L^1([a,b],\mathbb{R}^n)\to C([a,b],\mathbb{R}^n)\) is a linear integral operator. The main tool is a fixed point result due to the first author [Mat. Sb. 183, No. 10, 63-86 (1992; Zbl 0772.34017)].

MSC:
47H04 Set-valued operators
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
34A60 Ordinary differential inclusions
45N05 Abstract integral equations, integral equations in abstract spaces
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
47J05 Equations involving nonlinear operators (general)
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