The Fučík Spectrum for One Dimensional Kreĭn–Feller Operators

Abstract

In this article we study the Fučík spectrum for one dimensional Kreĭn–Feller operators, also known as measure-geometric Laplacians. We show the existence of a sequence of continuous and monotonic curves, and hyperbolic curves restricting their location. As a by-product, we give a different characterization of the eigenvalues of Kreĭn–Feller operators using nonlinear variational tools, and we show that they coincide with the ones obtained with the linear theory for compact operators in Hilbert spaces.