Existence and Nonexistence of Interior-Peaked Solution for a Nonlinear Neumann Problem

Title
Existence and Nonexistence of Interior-Peaked Solution for a Nonlinear Neumann Problem
Publication Date
2001
Author(s)
Cao, Daomin
Noussair, E S
Yan, Shusen
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Mathematical Sciences Publishers
Place of publication
United States of America
DOI
10.2140/pjm.2001.200.19
UNE publication id
une:13794
Abstract
We show that the critical problem {-∆υ + λυ = υ²*⁻¹ + αυq⁻¹, υ > 0 in Ω, ∂υ∕∂ν = 0 on ∂Ω, 2 < q < 2* = 2N/(N − 2), has no positive solutions concentrating, as λ → ∞, at interior points of Ω if a = 0, but for a class of symmetric domains Ω, the problem with α > 0 has solutions concentrating at interior points of Ω.
Link
link
Citation
Pacific Journal of Mathematics, 200(1), p. 19-42
ISSN
1945-5844
0030-8730
Start page
19
End page
42

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