A topological degree theory for perturbed AG(S+)-operators and applications to nonlinear problems
Let X be a real reflexive Banach space with X⁎ its dual space and G be a nonempty and open subset of X. Let A:X⊇D(A)→2X⁎ be a strongly quasibounded maximal monotone operator and T:X⊇D(T)→2X⁎ be an operator of class AG(S+) introduced by Kittilä. We develop a topological degree theory for the operator A+T. The theory generalizes the Browder degree theory for operators of type (S+) and extends the Kittilä degree theory for operators of class AG(S+). New existence results are established. The existence results give generalizations of similar known results for operators of type (S+). Applications to strongly nonlinear problems are included.
Journal of Mathematical Analysis and Applications
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