EXISTENCE AND UNIQUENESS RESULTS ON SINGLE-PEAKED SOLUTIONS OF A SEMILINEAR PROBLEM

Authors
CAO DM NOUSSAIR ES YAN SS
Citation
Dm. Cao et al., EXISTENCE AND UNIQUENESS RESULTS ON SINGLE-PEAKED SOLUTIONS OF A SEMILINEAR PROBLEM, Annales de l Institut Henri Poincare. Analyse non lineaire, 15(1), 1998, pp. 73-111
Citations number
12
Categorie Soggetti
Mathematics,Mathematics
Journal title
Annales de l Institut Henri Poincare. Analyse non lineaire → ACNP
ISSN journal
02941449
Volume
15
Issue
1
Year of publication
1998
Pages
73 - 111
Database
ISI
SICI code
0294-1449(1998)15:1<73:EAUROS>2.0.ZU;2-3
Abstract
A one to one correspondence is established between the nondegenerate c ritical points of Q(x) in Omega and single peaked solutions of the pro blem -epsilon(2) Delta u + u = Q(x)u(p-1) in Omega u > 0 in Omega and u = 0 on partial derivative Omega where Omega is a bounded domain, 2 < p < (N + 2)/(N - 2), epsilon > 0, and Q(x) epsilon C(<(Omega)over bar >) boolean AND C-2(Omega). In particular, we establish the uniqueness of the least energy solution when Q(x) attains its maximum in <(Omega) over bar> at only one nondegenerate critical point in Omega. (C) Elsev ier, Paris.