A new spectral theory for nonlinear operators and its applications

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.

Keywords

• Spectrum of a nonlinear operator
• eigenvalues
• (p,k)-epi mapping theory.