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On the Solvability of Inclusions with Multivalued Compact Perturbations of Bi-Mappings

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AbstractThis paper is about the solvability of the inclusion A(u,u)+F(u)∋L,$$A(u,u) + F(u) \ni L , $$ where X is a reflexive Banach space, L ∈ X∗, A is maximal monotone… Click to show full abstract

AbstractThis paper is about the solvability of the inclusion A(u,u)+F(u)∋L,$$A(u,u) + F(u) \ni L , $$ where X is a reflexive Banach space, L ∈ X∗, A is maximal monotone in one argument and continuous in the other argument in certain sense, and F is a multivalued perturbing term, which is compact in certain sense. We are interested in appropriate conditions on A and F such that this inclusion has solutions within a closed and convex set. We also prove that under such conditions the mapping u ↦ A (u, u) + F(u) is in fact generalized pseudomonotone in the sense of Browder and Hess (J. Funct. Anal. 11, 251–294, 1972).

Keywords: multivalued compact; compact perturbations; solvability inclusions; inclusions multivalued; solvability; perturbations mappings

Journal Title: Set-Valued and Variational Analysis
Year Published: 2019

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