In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.
V. K. Le, "A Range and Existence Theorem for Pseudomonotone Perturbations of Maximal Monotone Operators," Proceedings of the American Mathematical Society, American Mathematical Society, May 2011.
The definitive version is available at https://doi.org/10.1090/S0002-9939-2010-10594-4
Mathematics and Statistics
Keywords and Phrases
Pseudomonotone Perturbations; Range Theorem; Existence Theorems; Monotone Operators; Sobolev Spaces
Article - Journal
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