Generalized spectrum of Steklov-Robin problem for elliptic system

TL;DR

This paper investigates a generalized Steklov-Robin eigenvalue problem for elliptic systems with matrix weights, establishing the existence of an unbounded sequence of eigenvalues using variational methods.

Contribution

It introduces a generalized framework for the Steklov-Robin problem with matrix weights and proves the existence of an eigenvalue sequence, extending previous results.

Findings

Existence of an increasing unbounded sequence of eigenvalues.

Application of variational methods to elliptic systems with boundary spectral parameters.

Extension of classical Steklov-Robin problems to matrix-weighted systems.

Abstract

We will study the generalized Steklov Robin eigensystem (with possibly matrices weights) in which the spectral parameter is both in the system and on the boundary. We prove the existence of of an increasing unbounded sequence of eigenvalues .The method of proof makes use of variational arguments.