A priori bounds for positive solutions of a semilinear elliptic equation

Chris Cosner, Klaus Schmitt

Research output: Contribution to journalArticle

9 Scopus citations

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 - Sep 1985

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A priori bounds for positive solutions of a semilinear elliptic equation'. Together they form a unique fingerprint.

  • Cite this