On the Solvability of Inclusions with Multivalued Compact Perturbations of Bi-Mappings
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This paper is about the solvability of the inclusion
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).
$$A(u,u) + F(u) \ni L , $$
KeywordsInclusion Maximal monotone mapping Generalized pseudomonotone mapping Class (S)+ Multivalued mapping
Mathematics Subject Classifications (2010)58E35 47J20 47J25 35J87
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The author is very grateful for the referees’ careful reading of the manuscript and invaluable comments and suggestions.
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