Approximation Theorem for Principal Eigenvalue of Discrete $\pmb p$-Laplacian

TL;DR

This paper proves convergence of an approximation method and inverse iteration for the principal eigenvalue of discrete weighted p-Laplacian on nonnegative integers, with demonstrations through examples.

Contribution

It introduces a convergence proof for an approximation procedure and inverse iteration for the principal eigenvalue of discrete weighted p-Laplacian, including monotonicity analysis.

Findings

Convergence of approximation procedure established.

Inverse iteration method shown to converge.

Examples illustrate theoretical results.

Abstract

For the principal eigenvalue of discrete weighted $p$-Laplacian on the set of nonnegative integers, the convergence of an approximation procedure and the inverse iteration is proved. Meanwhile, in the proof of the convergence, the monotonicity of an approximation sequence is also checked. To illustrate these results, some examples are presented.