Citation
Yh. Du et Y. Lou, Proof of a conjecture for the perturbed Gelfand equation from combustion theory, J DIFF EQUA, 173(2), 2001, pp. 213-230
Citations number
22
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN journal
00220396
→ ACNP
Volume
173
Issue
2
Year of publication
2001
Pages
213 - 230
Database
ISI
SICI code
0022-0396(20010701)173:2<213:POACFT>2.0.ZU;2-O
Abstract
In this paper. we prove that when the domain B is a two dimensional ball. f
or all small positive epsilon, the solution curve ((lambda, u) of the pertu
rbed Gelfand equation - Deltau = lambda eu((1+epsilonu)) with u/(partial de
rivativeB) = 0 is exactly S-shaped. This settles along-standing conjecture
on the enact number of solutions to this equation. (C) 2001 Academic Press.