ABSTRACT
Let X be an infinite dimensional real reflexive Banach space with dual space and open and bounded. Let be a maximal monotone operator with and , and let be densely defined strongly quasibounded and of type . A new topological degree theory is introduced for the sum T+C with a degree mapping 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.
Disclosure statement
No potential conflict of interest was reported by the author.
ORCID
Dhruba R. Adhikari http://orcid.org/0000-0001-5871-694X