Perturbation of a single-valued operator by a multi-valued mapping of Hammerstein type with nonconvex images
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)].
scientific article; zbMATH DE number 1541446