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 |
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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
). |
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ISSN: | 1877-0533 1877-0541 |
DOI: | 10.1007/s11228-017-0431-x |