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 a...

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Veröffentlicht in:Set-valued and variational analysis 2019-03, Vol.27 (1), p.129-149
1. Verfasser: Le, Vy Khoi
Format: Artikel
Sprache:eng
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Zusammenfassung: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 ).
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-017-0431-x