Title

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

Abstract

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).

Department(s)

Mathematics and Statistics

Keywords and Phrases

Class (S) +; Generalized pseudomonotone mapping; Inclusion; Maximal monotone mapping; Multivalued mapping

International Standard Serial Number (ISSN)

0927-6947; 1572-932X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Springer Verlag, All rights reserved.

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