Convergence rates in a weighted Fucik problem

TL;DR

This paper investigates the convergence rates of the spectrum in a weighted Fučík problem under homogenization, providing explicit rates especially in the periodic case, with implications for boundary value problems.

Contribution

It introduces the analysis of spectral convergence rates in a weighted Fučík problem, including the periodic homogenization case, which is a novel contribution.

Findings

Derived the rate of convergence of the first non-trivial spectral curve.

Analyzed the homogenization of the spectrum for weighted Fučík problems.

Provided results for both Dirichlet and Neumann boundary conditions.

Abstract

In this work we consider the Fu\u{c}ik problem for a family of weights depending on $\ve$ with Dirichlet and Neumann boundary conditions. We study the homogenization of the spectrum. We also deal with the special case of periodic homogenization and we obtain the rate of convergence of the first non-trivial curve of the spectrum.