Some remarks on spectrum of nonlinear continuous operators

Abstract

In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study this question it is used a different approach that allows the studying of all eigenvalues of a nonlinear operator relative to another nonlinear operator. Here we show that in nonlinear operators case it is necessary to seek the spectrum of the given nonlinear operator relative to another nonlinear operator satisfying certain conditions. The different examples, for which eigenvalues can be found, are provided. Moreover, the nonlinear problems including parameters are studied.