Applications of Multiparameter Eigenvalue Problems

Abstract

It was mainly due to Atkinson works, who introduced Linear Multiparameter Eigenvalue problems (LMEPs), based on determinantal operators on the Tensor Product Space. Later, in the area of Multiparameter eigenvalue problems has received attention from the Mathematicians in the recent years also, who pointed out that there exist a variety of mixed eigenvalue problems with several parameters in different scientific domains. This article aims to bring into a light variety of scientific problems that appear naturally as LMEPs. Of course, with all certainty, the list of collection of applications presented here are far from complete, and there are bound to be many more applications of which we are currently unaware. The paper may provide a review on applications of Multiparameter eigenvalue problems in different scientific domains and future possible applicatios both in theoretical and applied disciplines.

On Nonlinearization of 3-parameter Eigenvalue Problems

“…here and z = x 1 ⊗ x 2 ⊗ x 3 is a decomposable tensor. Atkinson [2] investigated the problem of such kind carefully for i, j := 1 : k. The problem of this kind arises in diverse domain of science and engineering (e.g., [6]). Literature on the classical theory of multiparameter system has been reported in [2,9,25,35,36,38].…”