A Note on the Proof of the Perron-Frobenius Theorem

This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we observe that the conclusions of Perron-Frobenius theorem will hold if it holds for the starting matrix of this family. Based on our observations, we develop a simple numerical technique for approximating the Perron’s eigenpair of a given positive matrix. We apply the techniques introduced in the paper to approximate the Perron’s interval eigenvalue of a given positive interval matrix.

On the Spectrum of a Class of Strongly Coupled p-Laplacian Systems

Consider the nonlinear coupled elliptic system

A Note on Critical p-adic L-functions

We study the adjunction property of the Jacquet–Emerton functor in certain neighborhoods of critical points in the eigencurve.As an application,we construct two-variable p-adic L-functions around critical points via Emerton’s representation theoretic approach.