Exact multiplicity for boundary blow-up solutions

Zongming Guo; Feng Zhou

doi:10.1016/j.jde.2006.02.012

Exact multiplicity for boundary blow-up solutions

Zongming Guo
, Feng Zhou^*

^*Corresponding author for this work

School of Mathematical Sciences

Henan Normal University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

The singularly perturbed boundary blow-up problem- ε² Δ u = u (u - a) (1 - u), u > 0 in B, u = ∞ on ∂ B is studied in the unit ball B ⊂ R^N (N ≥ 2), a ∈ (1 / 2, 1) is a constant. It is shown that for ε > 0 sufficiently small, there exist exactly three positive solutions for the problem and all of them are radially symmetric solutions.

Original language	English
Pages (from-to)	486-506
Number of pages	21
Journal	Journal of Differential Equations
Volume	228
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2006.02.012
State	Published - 15 Sep 2006

Keywords

Boundary blow-up solutions
Exact multiplicity
Radial symmetry

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10.1016/j.jde.2006.02.012

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title = "Exact multiplicity for boundary blow-up solutions",

abstract = "The singularly perturbed boundary blow-up problem- ε2 Δ u = u (u - a) (1 - u), u > 0 in B, u = ∞ on ∂ B is studied in the unit ball B ⊂ RN (N ≥ 2), a ∈ (1 / 2, 1) is a constant. It is shown that for ε > 0 sufficiently small, there exist exactly three positive solutions for the problem and all of them are radially symmetric solutions.",

keywords = "Boundary blow-up solutions, Exact multiplicity, Radial symmetry",

author = "Zongming Guo and Feng Zhou",

year = "2006",

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language = "英语",

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AU - Guo, Zongming

AU - Zhou, Feng

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N2 - The singularly perturbed boundary blow-up problem- ε2 Δ u = u (u - a) (1 - u), u > 0 in B, u = ∞ on ∂ B is studied in the unit ball B ⊂ RN (N ≥ 2), a ∈ (1 / 2, 1) is a constant. It is shown that for ε > 0 sufficiently small, there exist exactly three positive solutions for the problem and all of them are radially symmetric solutions.

AB - The singularly perturbed boundary blow-up problem- ε2 Δ u = u (u - a) (1 - u), u > 0 in B, u = ∞ on ∂ B is studied in the unit ball B ⊂ RN (N ≥ 2), a ∈ (1 / 2, 1) is a constant. It is shown that for ε > 0 sufficiently small, there exist exactly three positive solutions for the problem and all of them are radially symmetric solutions.

KW - Boundary blow-up solutions

KW - Exact multiplicity

KW - Radial symmetry

UR - https://www.scopus.com/pages/publications/33746492315

U2 - 10.1016/j.jde.2006.02.012

DO - 10.1016/j.jde.2006.02.012

M3 - 文章

AN - SCOPUS:33746492315

SN - 0022-0396

VL - 228

SP - 486

EP - 506

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Exact multiplicity for boundary blow-up solutions

Abstract

Keywords

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