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https://hdl.handle.net/1959.11/5465
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DC Field | Value | Language |
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dc.contributor.author | Du, Yihong | en |
dc.contributor.author | Liu, Zhaoli | en |
dc.contributor.author | Pistoia, Angela | en |
dc.contributor.author | Yan, Shusen | en |
dc.date.accessioned | 2010-04-07T15:11:00Z | - |
dc.date.issued | 2008 | - |
dc.identifier.citation | Methods and Applications of Analysis, 15(2), p. 137-148 | en |
dc.identifier.issn | 1073-2772 | en |
dc.identifier.uri | https://hdl.handle.net/1959.11/5465 | - |
dc.description.abstract | We study sign changing solutions to equations of the form -∊²∆u+u=f(u) in B, ∂v u=0 on ∂B, where B is the unit ball in ℝ^N (N≥2), ∊ is a positive constant and f(u) behaves like |u|^p-1 u (but not necessarily odd) with 1 < p < (N+2)/(N-2) if N≥3, and 1 < p <∞ if N=2. We show that for any given positive integer n, this problem has a sign changing radial solution v∊(|x|) which changes sign at exactly n spheres ⋃^n/j=1 {|x|=ρ∊/j}, where 0 < ρ∊/1 < ⋯ < ρ∊/n < 1 and as ∊→0, ρ∊/j→0 and v∊→0 uniformly on compact subsets of (0,1]. Moreover, given any sequence ∊k→0, there is a subsequence ∊ki, such that u∊(|x|) converges to some U in C¹loc(ℝ^N) along this subsequence, and U=U(|x|) is a radial sign changing solution of -∆U+U=f(U) in ℝ^N, U ∈ H¹(ℝ^N) with exactly n zeros: 0 < ρ₁ < ⋯ < ρn < ∞, and ∊⁻¹ρ∊/j→pj along the subsequence ∊ki. Hence the sharp layers of the sign changing solution v∊ are clustered near the origin. The same result holds if the Neumann boundary condition is replaced by the Dirichlet boundary condition, or if B is replaced by ℝ^N. | en |
dc.language | en | en |
dc.publisher | International Press | en |
dc.relation.ispartof | Methods and Applications of Analysis | en |
dc.title | Sign Changing Solutions with Clustered Layers Near the Origin for Singularly Perturbed Semilinear Elliptic Problems On a Ball | en |
dc.type | Journal Article | en |
dc.subject.keywords | Partial Differential Equations | en |
local.contributor.firstname | Yihong | en |
local.contributor.firstname | Zhaoli | en |
local.contributor.firstname | Angela | en |
local.contributor.firstname | Shusen | en |
local.subject.for2008 | 010110 Partial Differential Equations | en |
local.subject.seo2008 | 970101 Expanding Knowledge in the Mathematical Sciences | en |
local.profile.school | School of Science and Technology | en |
local.profile.school | Maths | en |
local.profile.school | Maths | en |
local.profile.school | School of Science and Technology | en |
local.profile.email | ydu@une.edu.au | en |
local.profile.email | syan@une.edu.au | en |
local.output.category | C1 | en |
local.record.place | au | en |
local.record.institution | University of New England | en |
local.identifier.epublicationsrecord | une-20090721-173228 | en |
local.publisher.place | United States of America | en |
local.format.startpage | 137 | en |
local.format.endpage | 148 | en |
local.peerreviewed | Yes | en |
local.identifier.volume | 15 | en |
local.identifier.issue | 2 | en |
local.contributor.lastname | Du | en |
local.contributor.lastname | Liu | en |
local.contributor.lastname | Pistoia | en |
local.contributor.lastname | Yan | en |
dc.identifier.staff | une-id:ydu | en |
dc.identifier.staff | une-id:syan | en |
local.profile.orcid | 0000-0002-1235-0636 | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.profile.role | author | en |
local.identifier.unepublicationid | une:5595 | en |
dc.identifier.academiclevel | Academic | en |
dc.identifier.academiclevel | Academic | en |
local.title.maintitle | Sign Changing Solutions with Clustered Layers Near the Origin for Singularly Perturbed Semilinear Elliptic Problems On a Ball | en |
local.output.categorydescription | C1 Refereed Article in a Scholarly Journal | en |
local.relation.url | http://intlpress.com/site/pub/pages/journals/items/maa/content/vols/0015/0002/a002/index.html | en |
local.search.author | Du, Yihong | en |
local.search.author | Liu, Zhaoli | en |
local.search.author | Pistoia, Angela | en |
local.search.author | Yan, Shusen | en |
local.uneassociation | Unknown | en |
local.year.published | 2008 | en |
Appears in Collections: | Journal Article |
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