On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded-Reference-Cited by-同舟云学术

On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded

Published:2021-05-06 Issue:1-2 Volume:123 Page:79-94
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Esposito Luca¹,Roy Prosenjit²,Sk Firoj²

Affiliation:

1. DipMat, University of Salerno, Italy. E-mail: luesposi@unisa.it

2. Indian Institute of Technology, Kanpur, India. E-mails: prosenjit@iitk.ac.in, firoj@iitk.ac.in

Abstract

We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone identity to overcome nonlinearity complications. Altogether the use of Picone identity makes the proof easier with respect to the known proof in the linear case. Surprisingly the asymptotic behavior under mixed boundary conditions critically differs from the case of pure Dirichlet boundary conditions for some class of problems.

Publisher

IOS Press

Subject

General Mathematics

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