The Neumann boundary value problem of higher order quasilinear elliptic equation

Yongqiang Fu; Mei Yu

doi:10.1016/j.na.2010.02.024

The Neumann boundary value problem of higher order quasilinear elliptic equation

Yongqiang Fu
, Mei Yu^*

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

Abstract

This paper is concerned with the generalized solution to the Neumann boundary value problem of higher order quasilinear elliptic equation: {(under(∑, 1 ≤ | α | ≤ m) (- 1)^{| α |} D^α A_α (x, ξ_m (u)) = f (x, u),, x ∈ Ω,; B (x, ξ_m (u)) {dot operator} ν = g (x, u),, x ∈ ∂ Ω .) We show that there exists at least one non-trivial solution for the above problem in W^{m, p (x)} (Ω).

Original language	English
Pages (from-to)	4488-4499
Number of pages	12
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	72
Issue number	12
DOIs	https://doi.org/10.1016/j.na.2010.02.024
State	Published - 15 Jun 2010

Keywords

Embedding
L (Ω) space
W (Ω) space

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10.1016/j.na.2010.02.024

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abstract = "This paper is concerned with the generalized solution to the Neumann boundary value problem of higher order quasilinear elliptic equation: \{(under(∑, 1 ≤ | α | ≤ m) (- 1)| α | Dα Aα (x, ξm (u)) = f (x, u),, x ∈ Ω,; B (x, ξm (u)) \{dot operator\} ν = g (x, u),, x ∈ ∂ Ω .) We show that there exists at least one non-trivial solution for the above problem in Wm, p (x) (Ω).",

keywords = "Embedding, L (Ω) space, W (Ω) space",

author = "Yongqiang Fu and Mei Yu",

year = "2010",

month = jun,

day = "15",

doi = "10.1016/j.na.2010.02.024",

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volume = "72",

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T1 - The Neumann boundary value problem of higher order quasilinear elliptic equation

AU - Fu, Yongqiang

AU - Yu, Mei

PY - 2010/6/15

Y1 - 2010/6/15

N2 - This paper is concerned with the generalized solution to the Neumann boundary value problem of higher order quasilinear elliptic equation: {(under(∑, 1 ≤ | α | ≤ m) (- 1)| α | Dα Aα (x, ξm (u)) = f (x, u),, x ∈ Ω,; B (x, ξm (u)) {dot operator} ν = g (x, u),, x ∈ ∂ Ω .) We show that there exists at least one non-trivial solution for the above problem in Wm, p (x) (Ω).

AB - This paper is concerned with the generalized solution to the Neumann boundary value problem of higher order quasilinear elliptic equation: {(under(∑, 1 ≤ | α | ≤ m) (- 1)| α | Dα Aα (x, ξm (u)) = f (x, u),, x ∈ Ω,; B (x, ξm (u)) {dot operator} ν = g (x, u),, x ∈ ∂ Ω .) We show that there exists at least one non-trivial solution for the above problem in Wm, p (x) (Ω).

KW - Embedding

KW - L (Ω) space

KW - W (Ω) space

UR - https://www.scopus.com/pages/publications/77950369093

U2 - 10.1016/j.na.2010.02.024

DO - 10.1016/j.na.2010.02.024

M3 - 文章

AN - SCOPUS:77950369093

SN - 0362-546X

VL - 72

SP - 4488

EP - 4499

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -

The Neumann boundary value problem of higher order quasilinear elliptic equation

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Keywords

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