Existence of multiple positive solutions of semilinear elliptic boundary value problems in the half space

Tsing San Hsu; Huei Li Lin

doi:10.1016/j.na.2008.01.016

Existence of multiple positive solutions of semilinear elliptic boundary value problems in the half space

Tsing San Hsu^*
, Huei Li Lin

^*Corresponding author for this work

Center for General Education

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

4 Scopus citations

Abstract

In this paper, we prove that if Q and f satisfy some suitable conditions, then - Δ u + u = Q (x) f (u) in R₊^N with the boundary condition u (y, 0) = λ g (y) has at least two positive solutions if 0 < λ < λ^*, a unique positive solution if λ = λ^* and no positive solution if λ > λ^*.

Original language	English
Pages (from-to)	849-865
Number of pages	17
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	70
Issue number	2
DOIs	https://doi.org/10.1016/j.na.2008.01.016
State	Published - 15 01 2009

Keywords

Boundary value problems
Multiple positive solutions
Semilinear elliptic
The half space

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10.1016/j.na.2008.01.016

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title = "Existence of multiple positive solutions of semilinear elliptic boundary value problems in the half space",

abstract = "In this paper, we prove that if Q and f satisfy some suitable conditions, then - Δ u + u = Q (x) f (u) in R+N with the boundary condition u (y, 0) = λ g (y) has at least two positive solutions if 0 < λ < λ*, a unique positive solution if λ = λ* and no positive solution if λ > λ*.",

keywords = "Boundary value problems, Multiple positive solutions, Semilinear elliptic, The half space",

author = "Hsu, \{Tsing San\} and Lin, \{Huei Li\}",

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AU - Hsu, Tsing San

AU - Lin, Huei Li

PY - 2009/1/15

Y1 - 2009/1/15

N2 - In this paper, we prove that if Q and f satisfy some suitable conditions, then - Δ u + u = Q (x) f (u) in R+N with the boundary condition u (y, 0) = λ g (y) has at least two positive solutions if 0 < λ < λ*, a unique positive solution if λ = λ* and no positive solution if λ > λ*.

AB - In this paper, we prove that if Q and f satisfy some suitable conditions, then - Δ u + u = Q (x) f (u) in R+N with the boundary condition u (y, 0) = λ g (y) has at least two positive solutions if 0 < λ < λ*, a unique positive solution if λ = λ* and no positive solution if λ > λ*.

KW - Boundary value problems

KW - Multiple positive solutions

KW - Semilinear elliptic

KW - The half space

UR - https://www.scopus.com/pages/publications/56049109744

U2 - 10.1016/j.na.2008.01.016

DO - 10.1016/j.na.2008.01.016

M3 - 文章

AN - SCOPUS:56049109744

SN - 0362-546X

VL - 70

SP - 849

EP - 865

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 2

ER -

Existence of multiple positive solutions of semilinear elliptic boundary value problems in the half space

Abstract

Keywords

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