Dhruba R. Adhikari
Abstract:
Let
be a real reflexive Banach space and
its dual space.
Let
be an operator of class
,
where
.
A result concerning the existence of pathwise
connected sets in the range of T is established, and as a consequence,
an open mapping theorem is proved. In addition, for certain operators
T of class
,
the existence of nonzero solutions of
in
,
where
satisfy
and
,
is established. The Skrypnik's topological
degree theory is used, utilizing approximating schemes for operators
of classes
and
,
along with the methodology of a recent invariance of domain result by Kartsatos
and the author.
Published November 15, 2017.
Math Subject Classifications: 47H14, 47H05, 47H11.
Key Words: Browder and Skrypnik degree theory; invariance of domain;
nonzero solutions; bounded demicontinuous operator of type (S+).
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Dhruba R. Adhikari Department of Mathematics Kennesaw State University Georgia 30060, USA email: dadhikar@kennesaw.edu |
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