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^*

^*此作品的通讯作者

数学科学学院

Henan Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	486-506
页数	21
期刊	Journal of Differential Equations
卷	228
期	2
DOI	https://doi.org/10.1016/j.jde.2006.02.012
出版状态	已出版 - 15 9月 2006

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10.1016/j.jde.2006.02.012

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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.",

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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

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VL - 228

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EP - 506

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Exact multiplicity for boundary blow-up solutions

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