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 ) → 2 X ⁎ be a strongly quasibounded maximal monotone operator and T : X ⊇ D ( T ) → 2 X ⁎ be an operator of class A G ( S + ) introduced by Kittila. 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 Kittila degree theory for operators of class A G ( 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.