Let X be a real reflexive locally uniformly convex
Banach space with locally uniformly convex dual space X*
. Let G be a
bounded open subset of X. Let T:X⊃ D(T)⇒ 2X*
be maximal
monotone and S: X ⇒ 2X*
be bounded
pseudomonotone and such that 0 notin cl((T+S)(D(T)∩partG)). Chapter 1 gives general introduction and mathematical prerequisites. In
Chapter 2 we develop a homotopy invariance and uniqueness results for the degree theory constructed by Zhang and Chen for multivalued (S+) perturbations of
maximal monotone operators. Chapter 3 is devoted to the construction of a new topological degree
theory for the sum T+S with the degree mapping d(T+S,G,0) defined by
d(T+S,G,0)=limepsilondarr
0+
dS+(T+S+ J,G,0),
where dS+ is the degree for bounded (S+)-perturbations of maximal
monotone operators. The uniqueness and homotopy invariance result of
this degree mapping are also included herein. As applications of the theory, we give associated mapping theorems as well as degree theoretic
proofs of known results by Figueiredo, Kenmochi and Le.
In chapter 4, we consider T:X D(T)⇒ 2X*
to be maximal monotone and S:D(S)=K⇒ 2X*
at least pseudomonotone, where K is a nonempty, closed
and convex subset of X with 0isinKordm. Let Phi:X⇒ ( infin, infin] be a
proper, convex and lower-semicontinuous function. Let f*
isin X*
be fixed. New
results are given concerning the solvability of perturbed variational inequalities
for operators of the type T+S associated with the function f. The associated
range results for nonlinear operators are also given, as well as extensions and/or
improvements of known results by Kenmochi, Le, Browder, Browder and Hess,
Figueiredo, Zhou, and others.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-5630 |
| Date | 01 January 2013 |
| Creators | Asfaw, Teffera Mekonnen |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
| Rights | default |
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