A new class of eigenvalue problems for perturbed p-Laplacians

TL;DR

This paper introduces a novel class of eigenvalue problems for perturbed p-Laplacians, providing new analytical techniques, dispersion relations, and variational principles, with applications to real-world problems.

Contribution

It develops original methods to solve non-standard eigenvalue problems for perturbed p-Laplacians, expanding beyond traditional nonlinear eigenvalue approaches.

Findings

Derived dispersion relations between eigen-parameters

Provided quantitative analysis of eigenvectors

Established variational principles for eigenvalues

Abstract

This paper is devoted to a dispersion analysis of a class of perturbed p-Laplacians. Besides the p-Laplacian-like eigenvalue problems we also deal with new and non-standard eigenvalue problems, which can not be solved by the methods used in nonlinear eigenvalue problems for p-Laplacians and similar operators. Original techniques are suggested for solving these new problems (see Section 3). In addition, dispersion relations between the eigen-parameters, quantitative analysis of eigenvectors and variational principles for eigenvalues of perturbed p-Laplacians are also studied in this paper. The problems, we study in this paper arise from the real world problems.