Topological degree for quasibounded multivalued (S̃)+-perturbations of maximal monotone operators
© 2018 Informa UK Limited, trading as Taylor & Francis Group. Let X be an infinite dimensional real reflexive Banach space with dual space (Formula presented.) and (Formula presented.) open and bounded. Let (Formula presented.) be a maximal monotone operator with (Formula presented.) and (Formula presented.), and let (Formula presented.) be densely defined strongly quasibounded and of type (Formula presented.). A new topological degree theory is introduced for the sum T+C with a degree mapping (Formula presented.) defined eventually in terms of the Ma degree for multivalued compact operators. Unlike single-valued operators considered by Kartsatos and Skrypnik, the operator C here is multivalued so that the multivalued generalized pseudomonotone operators considered by Browder and Hess include such C and even T+C. Consequently, the main existence results of Browder and Hess are obtained via the new degree theory and some of their existence results are extended. An application of the theory to elliptic partial differential inclusions in divergence form is included.
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