Solutions of semilinear elliptic equations with asymptotic linear nonlinearity

Cheng Hsiung Hsu; Yi Wen Shih

doi:10.1016/S0362-546X(01)00759-3

Solutions of semilinear elliptic equations with asymptotic linear nonlinearity

Cheng Hsiung Hsu, Yi Wen Shih

Department of Mathematics

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

3 Scopus citations

Abstract

The existence, uniqueness and asymptotic behavior of positive solutions of the semilinear elliptic equations with asymptotic linear nonlinearity was studied. It was proved that if ε > 0, then there existed exactly one solution u_λ(.,ε) for all λ ∈ (0,λ₁) where λ₁ represents first eignvalue of -δ in ω with Dirichlet boundary condition. The results showed that if s < t and small enough, δū+λf_ε(ū) < -s + ||h(ū)||_∞ ≤ 0 was found by choosing δ = s.

Original language	English
Pages (from-to)	275-283
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	50
Issue number	2
DOIs	https://doi.org/10.1016/S0362-546X(01)00759-3
State	Published - Jul 2002

Keywords

Hopf lemma
Minimal solution
Perturbation lemma
Variation method of Nehari-type

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10.1016/S0362-546X(01)00759-3

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title = "Solutions of semilinear elliptic equations with asymptotic linear nonlinearity",

abstract = "The existence, uniqueness and asymptotic behavior of positive solutions of the semilinear elliptic equations with asymptotic linear nonlinearity was studied. It was proved that if ε > 0, then there existed exactly one solution uλ(.,ε) for all λ ∈ (0,λ1) where λ1 represents first eignvalue of -δ in ω with Dirichlet boundary condition. The results showed that if s < t and small enough, δū+λfε(ū) < -s + ||h(ū)||∞ ≤ 0 was found by choosing δ = s.",

keywords = "Hopf lemma, Minimal solution, Perturbation lemma, Variation method of Nehari-type",

author = "Hsu, {Cheng Hsiung} and Shih, {Yi Wen}",

note = "Funding Information: Work partially supported by the National Science Council of the Republic of China. ",

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TY - JOUR

T1 - Solutions of semilinear elliptic equations with asymptotic linear nonlinearity

AU - Hsu, Cheng Hsiung

AU - Shih, Yi Wen

N1 - Funding Information: Work partially supported by the National Science Council of the Republic of China.

PY - 2002/7

Y1 - 2002/7

N2 - The existence, uniqueness and asymptotic behavior of positive solutions of the semilinear elliptic equations with asymptotic linear nonlinearity was studied. It was proved that if ε > 0, then there existed exactly one solution uλ(.,ε) for all λ ∈ (0,λ1) where λ1 represents first eignvalue of -δ in ω with Dirichlet boundary condition. The results showed that if s < t and small enough, δū+λfε(ū) < -s + ||h(ū)||∞ ≤ 0 was found by choosing δ = s.

AB - The existence, uniqueness and asymptotic behavior of positive solutions of the semilinear elliptic equations with asymptotic linear nonlinearity was studied. It was proved that if ε > 0, then there existed exactly one solution uλ(.,ε) for all λ ∈ (0,λ1) where λ1 represents first eignvalue of -δ in ω with Dirichlet boundary condition. The results showed that if s < t and small enough, δū+λfε(ū) < -s + ||h(ū)||∞ ≤ 0 was found by choosing δ = s.

KW - Hopf lemma

KW - Minimal solution

KW - Perturbation lemma

KW - Variation method of Nehari-type

UR - http://www.scopus.com/inward/record.url?scp=0036642749&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(01)00759-3

DO - 10.1016/S0362-546X(01)00759-3

M3 - 期刊論文

AN - SCOPUS:0036642749

VL - 50

SP - 275

EP - 283

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 2

ER -

Solutions of semilinear elliptic equations with asymptotic linear nonlinearity

Abstract

Keywords

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