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Eighth Mississippi State - UAB Conference on Differential Equations & Computational Simulations
May 7-9, 2009
Department of Mathematics and Statistics, Mississippi State University
Mississippi State, MS, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Invariance of Domain and Eigenvalues for Perturbations of Densely Defined Linear Maximal Monotone Operators
by
Dhruba Adhikari
Mississippi University for Women
Coauthors: Athanassios G. Kartsatos

Let X be a real reflexive Banach space with dual X*. Let L: X ⊃ D(L) → X* be densely defined linear maximal monotone. Let T: X ⊃ D(T) → 2X* be maximal monotone with 0 ∈ \overset ○D(T) and 0 ∈ T(0), and C: X ⊃ D(C) → X* bounded, demicontinuous and of type (S+) w.r.t. D(L). An invariance of domain result has been established for the sum L+T+C. An eigenvalue problem of the type Lx + Tx + C(l, x) ∍ 0 is also solved, where T is now maximal monotone and strongly quasibounded with 0 ∈ T(0) and C(l, ·), l > 0, is like C above. The recent topological degree theory of the authors is used, utilizing the graph norm topology on D(L), along with the methodology of Berkovits and Mustonen and recent invariance of domain and eigenvalue results by Kartsatos and Skrypnik. Possible applications to time-dependent problems are also included.

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Date received: March 29, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxp-91.