Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841053 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 15 Pages |
Abstract
Let X be a real reflexive separable locally uniformly convex Banach space with locally uniformly convex dual space Xâ. Let Q:HâX be a linear compact injection, according to Browder and Ton, such that Q(H)¯=X, where H is a real separable Hilbert space. A degree mapping d on X is constructed from the Nagumo degree dNA on H by d(T+f,G,0)âlimtâ0dNA(I+1tQâ(Tt+f)Q,Qâ1G,0), where GâX is open and bounded, Tt is the resolvent (Tâ1+tJâ1)â1 of a strongly quasibounded maximal monotone operator T:XâD(T)â2Xâ with 0âT(0), and f:G¯âXâ is demicontinuous, bounded and of type (S+). A “range of sums” result is also given, using the Skrypnik degree theory, in order to further exhibit the methodology of “elliptic super-regularization”.
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Authors
Athanassios G. Kartsatos, David Kerr,