The spectrum in $R$ and $R^2$ of nonlinear elliptic equations with positive parameters

Abstract

In this paper we study the spectrum in $\R$ and $\R^2$ of nonlinear elliptic equations with positive parameters in their nonlinear part. In order to investigate the spectrum in these specific cases, we introduce the monotone method which is an extension of the upper and lower solution methods. Using the Picard iterative process we prove some existence theorems for nonlinear elliptic boundary value problems. We work with both positive and negative solutions.