Existence and multiplicity of positive solutions for a class of elliptic boundary value problems in the half-space

Tsing San Hsu

doi:10.1515/ans-2007-0202

Existence and multiplicity of positive solutions for a class of elliptic boundary value problems in the half-space

Tsing San Hsu^*

^*Corresponding author for this work

Center for General Education

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

2 Scopus citations

Abstract

In this paper, we prove that if b(x) satisfies some suitable conditions, then -Δu + u = b(x)u^p in ℝ₊^N with the boundary condition u(xλ,0) = Γg(x′) has at least two positive solutions if 0 < λ < λ*, a minimal positive solution if λ = λ* and no positive solution if λ> λ*.

Original language	English
Pages (from-to)	187-209
Number of pages	23
Journal	Advanced Nonlinear Studies
Volume	7
Issue number	2
DOIs	https://doi.org/10.1515/ans-2007-0202
State	Published - 05 2007

Keywords

Elliptic boundary value problems
Existence
Multiplicity
The half space

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title = "Existence and multiplicity of positive solutions for a class of elliptic boundary value problems in the half-space",

abstract = "In this paper, we prove that if b(x) satisfies some suitable conditions, then -Δu + u = b(x)up in ℝ+N with the boundary condition u(xλ,0) = Γg(x′) has at least two positive solutions if 0 < λ < λ*, a minimal positive solution if λ = λ* and no positive solution if λ> λ*.",

keywords = "Elliptic boundary value problems, Existence, Multiplicity, The half space",

author = "Hsu, \{Tsing San\}",

year = "2007",

month = may,

doi = "10.1515/ans-2007-0202",

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AU - Hsu, Tsing San

PY - 2007/5

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N2 - In this paper, we prove that if b(x) satisfies some suitable conditions, then -Δu + u = b(x)up in ℝ+N with the boundary condition u(xλ,0) = Γg(x′) has at least two positive solutions if 0 < λ < λ*, a minimal positive solution if λ = λ* and no positive solution if λ> λ*.

AB - In this paper, we prove that if b(x) satisfies some suitable conditions, then -Δu + u = b(x)up in ℝ+N with the boundary condition u(xλ,0) = Γg(x′) has at least two positive solutions if 0 < λ < λ*, a minimal positive solution if λ = λ* and no positive solution if λ> λ*.

KW - Elliptic boundary value problems

KW - Existence

KW - Multiplicity

KW - The half space

UR - https://www.scopus.com/pages/publications/34247267721

U2 - 10.1515/ans-2007-0202

DO - 10.1515/ans-2007-0202

M3 - 文章

AN - SCOPUS:34247267721

SN - 1536-1365

VL - 7

SP - 187

EP - 209

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

IS - 2

ER -

Existence and multiplicity of positive solutions for a class of elliptic boundary value problems in the half-space

Abstract

Keywords

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