Dhruba R. Adhikari
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
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