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Abstract and Applied Analysis
Volume 2, Issue 1-2, Pages 163-183
http://dx.doi.org/10.1155/S1085337597000328

A new spectral theory for nonlinear operators and its applications

Department of Mathematics, University of South Florida, Tampa 33620-5700, FL, USA

Received 1 September 1997

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, by applying (p,k)-epi mapping theory, we introduce a new definition of spectrum for nonlinear operators which contains all eigenvalues, as in the linear case. Properties of this spectrum are given and comparison is made with the other definitions of spectra. We also give applications of the new theory.