On the neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type

Wei Ming Ni, Izumi Takagi

Research output: Contribution to journalArticlepeer-review

77 Scopus citations

Abstract

We derive a priori estimates for positive solutions of the Neumann problem for some semilinear elliptic systems (i.e., activator-inhibitor systems in biological pattern formation theory), as well as for semilinear single equations related to such systems. By making use of these a priori estimates, we show that under certain assumptions, there is no positive nonconstant solutions for single equations or for activator-inhibitor systems when the diffusion coefficient (of the activator, in the case of systems) is sufficiently large; we also study the existence of nonconstant solutions for specific domains.

Original languageEnglish (US)
Pages (from-to)351-368
Number of pages18
JournalTransactions of the American Mathematical Society
Volume297
Issue number1
DOIs
StatePublished - Sep 1986

Fingerprint Dive into the research topics of 'On the neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type'. Together they form a unique fingerprint.

Cite this