Nonradial solutions for a conformally invariant fourth order equation in ℝ4

Juncheng Wei; Dong Ye

doi:10.1007/s00526-007-0145-2

Nonradial solutions for a conformally invariant fourth order equation in ℝ⁴

Juncheng Wei^*
, Dong Ye

^*Corresponding author for this work

Chinese University of Hong Kong
CY Cergy Paris Université

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

47 Scopus citations

Abstract

We consider the following Liouville equation in ℝ⁴ Δ²u = 6e^4u in ℝ⁴, ∫ ℝ⁴ e^4udx < . For each fixed x⁰ ∞ ℝ⁴, 1 ≤ k ≤ 4, α (1-k/4, 2) and a _j > 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior: u(x) = - ∑_j=1^ka _j x_j - x_j⁰² - αlog,|x|+c0 + o(1), |x| > 1,∫ ℝ⁴ e ^4u(x)}dx= 4π²α3.

Original language	English
Pages (from-to)	373-386
Number of pages	14
Journal	Calculus of Variations and Partial Differential Equations
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s00526-007-0145-2
State	Published - Jul 2008
Externally published	Yes

Access to Document

10.1007/s00526-007-0145-2

Cite this

@article{613fdadb9f054a9f983bc6d313d18845,

title = "Nonradial solutions for a conformally invariant fourth order equation in ℝ4",

abstract = "We consider the following Liouville equation in ℝ4 Δ2u = 6e4u in ℝ4, ∫ ℝ4 e4udx < . For each fixed x0 ∞ ℝ4, 1 ≤ k ≤ 4, α (1-k/4, 2) and a j > 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior: u(x) = - ∑j=1ka j xj - xj02 - αlog,|x|+c0 + o(1), |x| > 1,∫ ℝ4 e 4u(x)\}dx= 4π2α3.",

author = "Juncheng Wei and Dong Ye",

year = "2008",

month = jul,

doi = "10.1007/s00526-007-0145-2",

language = "英语",

volume = "32",

pages = "373--386",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - Nonradial solutions for a conformally invariant fourth order equation in ℝ4

AU - Wei, Juncheng

AU - Ye, Dong

PY - 2008/7

Y1 - 2008/7

N2 - We consider the following Liouville equation in ℝ4 Δ2u = 6e4u in ℝ4, ∫ ℝ4 e4udx < . For each fixed x0 ∞ ℝ4, 1 ≤ k ≤ 4, α (1-k/4, 2) and a j > 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior: u(x) = - ∑j=1ka j xj - xj02 - αlog,|x|+c0 + o(1), |x| > 1,∫ ℝ4 e 4u(x)}dx= 4π2α3.

AB - We consider the following Liouville equation in ℝ4 Δ2u = 6e4u in ℝ4, ∫ ℝ4 e4udx < . For each fixed x0 ∞ ℝ4, 1 ≤ k ≤ 4, α (1-k/4, 2) and a j > 0 for 1 ≤ j ≤ k, we construct a solution to the above equation with the following asymptotic behavior: u(x) = - ∑j=1ka j xj - xj02 - αlog,|x|+c0 + o(1), |x| > 1,∫ ℝ4 e 4u(x)}dx= 4π2α3.

UR - https://www.scopus.com/pages/publications/42449114868

U2 - 10.1007/s00526-007-0145-2

DO - 10.1007/s00526-007-0145-2

M3 - 文章

AN - SCOPUS:42449114868

SN - 0944-2669

VL - 32

SP - 373

EP - 386

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 3

ER -

Nonradial solutions for a conformally invariant fourth order equation in ℝ⁴

Abstract

Access to Document

Other files and links

Fingerprint

Cite this