We are concerned in this article with the existence of solutions to inclusions containing generalized pseudomonotone perturbations of maximal monotone mappings in general Banach spaces. Our approach is based on a truncation–regularization technique and an extension of the Moreau–Yosida–Brezis–Crandall–Pazy regularization for maximal monotone mappings in general Banach spaces. We also consider some applications to multivalued variational inequalities containing elliptic operators with rapidly growing coefficients in Orlicz–Sobolev spaces.
V. K. Le, "On Inclusions with Monotone-Type Mappings in Nonreflexive Banach Spaces," Journal of Optimization Theory and Applications, vol. 192, no. 2, pp. 484 - 509, Springer, Feb 2022.
The definitive version is available at https://doi.org/10.1007/s10957-021-01973-1
Mathematics and Statistics
Keywords and Phrases
Monotone mapping; Multivalued mapping; Nonreflexive Banach space; Orlicz–Sobolev space; Variational inequality
International Standard Serial Number (ISSN)
Article - Journal
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01 Feb 2022