Existence of Continuous Eigenvalues for a Class of Parametric Problems Involving the (p, 2) -Laplacian Operator

Tilak Bhattacharya, Behrouz Emamizadeh, Amin Farjudian

Research output: Journal PublicationArticlepeer-review

5 Citations (Scopus)
4 Downloads (Pure)

Abstract

We discuss a parametric eigenvalue problem, where the differential operator is of (p, 2) -Laplacian type. We show that, when p≠ 2 , the spectrum of the operator is a half line, with the end point formulated in terms of the parameter and the principal eigenvalue of the Laplacian with zero Dirichlet boundary conditions. Two cases are considered corresponding to p> 2 and p< 2 , and the methods that are applied are variational. In the former case, the direct method is applied, whereas in the latter case, the fibering method of Pohozaev is used. We will also discuss a priori bounds and regularity of the eigenfunctions. In particular, we will show that, when the eigenvalue tends towards the end point of the half line, the supremum norm of the corresponding eigenfunction tends to zero in the case of p> 2 , and to infinity in the case of p< 2.

Original languageEnglish
Pages (from-to)65-79
Number of pages15
JournalActa Applicandae Mathematicae
Volume165
Issue number1
DOIs
Publication statusPublished - 1 Feb 2020

Keywords

  • Continuous eigenvalues
  • Fibering method
  • p-Laplacian

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Existence of Continuous Eigenvalues for a Class of Parametric Problems Involving the (p, 2) -Laplacian Operator'. Together they form a unique fingerprint.

Cite this