On the Solvability of Inclusions with Multivalued Compact Perturbations of Bi-Mappings
This paper is about the solvability of the inclusion A(u, u) + F(u) ∋ 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).
V. K. Le, "On the Solvability of Inclusions with Multivalued Compact Perturbations of Bi-Mappings," Set-Valued and Variational Analysis, vol. 27, no. 1, pp. 129-149, Springer Verlag, Mar 2019.
The definitive version is available at https://doi.org/10.1007/s11228-017-0431-x
Mathematics and Statistics
Keywords and Phrases
Class (S) +; Generalized pseudomonotone mapping; Inclusion; Maximal monotone mapping; Multivalued mapping
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2019