Asymptotic behavior of positive solutions to semilinear elliptic equations on expanding annuli

Song-Sun Lin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We study the asymptotic behavior of positive solutions of the semilinear elliptic equation Δu + f(u) = 0 in Ωa, u = 0 on ∂Ωa, where Ωa = (x ∈ of RN: a < |x| < a + 1) are expanding annuli as a → ∞, and ƒ is positive and superlinear at both 0 and ∞. We first show that there are a priori bounds for some positive solutions ua(x) as a → ∞. Then, if we fix any direction, after a suitable translation of ua the limiting solutions are non-negative solutions on the infinite strip. We can obtain more detailed descriptions of these limits if ua is radially symmetric, least-energy, or least-energy with a particular symmetry.

Original languageEnglish
Pages (from-to)255-288
Number of pages34
JournalJournal of Differential Equations
Volume120
Issue number2
DOIs
StatePublished - 1 Jan 1995

Fingerprint Dive into the research topics of 'Asymptotic behavior of positive solutions to semilinear elliptic equations on expanding annuli'. Together they form a unique fingerprint.

Cite this