A priori bounds for positive solutions of a semilinear elliptic equation

George Cosner, Klaus Schmitt

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

Original languageEnglish (US)
Pages (from-to)70-73
Number of pages4
JournalProceedings of the American Mathematical Society
Volume95
Issue number1
DOIs
StatePublished - 1985

Fingerprint

A Priori Bounds
Semilinear Elliptic Equations
Dirichlet Boundary Conditions
Positive Solution
Bounded Domain
Boundary conditions
Nonlinearity
Lower bound
Norm
Symmetry
Zero

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A priori bounds for positive solutions of a semilinear elliptic equation. / Cosner, George; Schmitt, Klaus.

In: Proceedings of the American Mathematical Society, Vol. 95, No. 1, 1985, p. 70-73.

Research output: Contribution to journalArticle

@article{e5ef91b98eea456f89e1e63731bdbb13,
title = "A priori bounds for positive solutions of a semilinear elliptic equation",
abstract = "We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.",
author = "George Cosner and Klaus Schmitt",
year = "1985",
doi = "10.1090/S0002-9939-1985-0796444-0",
language = "English (US)",
volume = "95",
pages = "70--73",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "1",

}

TY - JOUR

T1 - A priori bounds for positive solutions of a semilinear elliptic equation

AU - Cosner, George

AU - Schmitt, Klaus

PY - 1985

Y1 - 1985

N2 - We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

AB - We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

UR - http://www.scopus.com/inward/record.url?scp=84864263679&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864263679&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1985-0796444-0

DO - 10.1090/S0002-9939-1985-0796444-0

M3 - Article

AN - SCOPUS:84864263679

VL - 95

SP - 70

EP - 73

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -