Existence of weak solutions for a fourth-order Navier boundary value problem

Jiafa Xu; Wei Dong; Donal O'Regan

doi:10.1016/j.aml.2014.01.003

Existence of weak solutions for a fourth-order Navier boundary value problem

Jiafa Xu
, Wei Dong
, Donal O'Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we discuss the existence of weak solutions for the fourth-order Navier boundary value problem {^Δ2u(x)+cΔu(x) =λu(x)+f(u(x)),in Ω,u=Δu=0,on ∂Ω, where λ is a parameter, ^Δ2 is the biharmonic operator, Ω⊂^RN(N>4) is a smooth bounded domain, and -rffrtεC(R,R). We use topological degree theory and critical point theory to establish the existence.

Original language	English
Pages (from-to)	61-66
Number of pages	6
Journal	Applied Mathematics Letters
Volume	37
DOIs	https://doi.org/10.1016/j.aml.2014.01.003
Publication status	Published - Nov 2014

Keywords

Critical point theory
Navier boundary value problem
Topological degree theory
Weak solution

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10.1016/j.aml.2014.01.003

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title = "Existence of weak solutions for a fourth-order Navier boundary value problem",

abstract = "In this paper we discuss the existence of weak solutions for the fourth-order Navier boundary value problem \{Δ2u(x)+cΔu(x) =λu(x)+f(u(x)),in Ω,u=Δu=0,on ∂Ω, where λ is a parameter, Δ2 is the biharmonic operator, Ω⊂RN(N>4) is a smooth bounded domain, and -rffrtεC(R,R). We use topological degree theory and critical point theory to establish the existence.",

keywords = "Critical point theory, Navier boundary value problem, Topological degree theory, Weak solution",

author = "Jiafa Xu and Wei Dong and Donal O'Regan",

year = "2014",

month = nov,

doi = "10.1016/j.aml.2014.01.003",

language = "English",

volume = "37",

pages = "61--66",

journal = "Applied Mathematics Letters",

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T1 - Existence of weak solutions for a fourth-order Navier boundary value problem

AU - Xu, Jiafa

AU - Dong, Wei

AU - O'Regan, Donal

PY - 2014/11

Y1 - 2014/11

N2 - In this paper we discuss the existence of weak solutions for the fourth-order Navier boundary value problem {Δ2u(x)+cΔu(x) =λu(x)+f(u(x)),in Ω,u=Δu=0,on ∂Ω, where λ is a parameter, Δ2 is the biharmonic operator, Ω⊂RN(N>4) is a smooth bounded domain, and -rffrtεC(R,R). We use topological degree theory and critical point theory to establish the existence.

AB - In this paper we discuss the existence of weak solutions for the fourth-order Navier boundary value problem {Δ2u(x)+cΔu(x) =λu(x)+f(u(x)),in Ω,u=Δu=0,on ∂Ω, where λ is a parameter, Δ2 is the biharmonic operator, Ω⊂RN(N>4) is a smooth bounded domain, and -rffrtεC(R,R). We use topological degree theory and critical point theory to establish the existence.

KW - Critical point theory

KW - Navier boundary value problem

KW - Topological degree theory

KW - Weak solution

UR - https://www.scopus.com/pages/publications/84902513763

U2 - 10.1016/j.aml.2014.01.003

DO - 10.1016/j.aml.2014.01.003

M3 - Article

SN - 0893-9659

VL - 37

SP - 61

EP - 66

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Existence of weak solutions for a fourth-order Navier boundary value problem

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Keywords

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