Estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider solutions to the nonlinear eigenvalue problem (*) [FORMULA PRESENT], where (*) is a quasilinear strongly coupled second order elliptic system of partial differential equations and Ω ⊆ Rn is a smooth bounded domain. We obtain lower bounds for λ in the case where f(x, u) has linear growth, and relations between λ,Ω and ess sup |u| when f(x, u) has sub- or superlinear growth. The estimates are based on integration by parts and application of certain Sobolev inequalities. We briefly discuss extensions to' higher order systems.

Original languageEnglish (US)
Pages (from-to)59-75
Number of pages17
JournalTransactions of the American Mathematical Society
Volume282
Issue number1
DOIs
StatePublished - 1984

Fingerprint

Nonlinear Elliptic Problems
Eigenvalues and Eigenfunctions
Eigenvalues and eigenfunctions
Integration by parts
Nonlinear Eigenvalue Problem
Sobolev Inequality
Second-order Systems
Systems of Partial Differential Equations
Elliptic Systems
Estimate
Partial differential equations
Bounded Domain
Higher Order
Lower bound

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems. / Cosner, George.

In: Transactions of the American Mathematical Society, Vol. 282, No. 1, 1984, p. 59-75.

Research output: Contribution to journalArticle

@article{172ba87ec61f4538bd73265c7bc45944,
title = "Estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems",
abstract = "We consider solutions to the nonlinear eigenvalue problem (*) [FORMULA PRESENT], where (*) is a quasilinear strongly coupled second order elliptic system of partial differential equations and Ω ⊆ Rn is a smooth bounded domain. We obtain lower bounds for λ in the case where f(x, u) has linear growth, and relations between λ,Ω and ess sup |u| when f(x, u) has sub- or superlinear growth. The estimates are based on integration by parts and application of certain Sobolev inequalities. We briefly discuss extensions to' higher order systems.",
author = "George Cosner",
year = "1984",
doi = "10.1090/S0002-9947-1984-0728703-5",
language = "English (US)",
volume = "282",
pages = "59--75",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "1",

}

TY - JOUR

T1 - Estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems

AU - Cosner, George

PY - 1984

Y1 - 1984

N2 - We consider solutions to the nonlinear eigenvalue problem (*) [FORMULA PRESENT], where (*) is a quasilinear strongly coupled second order elliptic system of partial differential equations and Ω ⊆ Rn is a smooth bounded domain. We obtain lower bounds for λ in the case where f(x, u) has linear growth, and relations between λ,Ω and ess sup |u| when f(x, u) has sub- or superlinear growth. The estimates are based on integration by parts and application of certain Sobolev inequalities. We briefly discuss extensions to' higher order systems.

AB - We consider solutions to the nonlinear eigenvalue problem (*) [FORMULA PRESENT], where (*) is a quasilinear strongly coupled second order elliptic system of partial differential equations and Ω ⊆ Rn is a smooth bounded domain. We obtain lower bounds for λ in the case where f(x, u) has linear growth, and relations between λ,Ω and ess sup |u| when f(x, u) has sub- or superlinear growth. The estimates are based on integration by parts and application of certain Sobolev inequalities. We briefly discuss extensions to' higher order systems.

UR - http://www.scopus.com/inward/record.url?scp=84967713485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84967713485&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1984-0728703-5

DO - 10.1090/S0002-9947-1984-0728703-5

M3 - Article

VL - 282

SP - 59

EP - 75

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -