A note on a class of higher order conformally covariant equations

Sun Yung Alice Chang; Wenxiong Chen

doi:10.3934/dcds.2001.7.275

A note on a class of higher order conformally covariant equations

Sun Yung Alice Chang, Wenxiong Chen

Mathematics

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64 Scopus citations

Abstract

In this paper, we study the higher order conformally covariant equation (- Δ)^n/2 w = (n - 1)!e^nw x ∈ Rⁿ for all even dimensions n. Let a = 1/|Sⁿ| ∫_Rn e^nw dx. We prove, for every 0 < a < 1, the existence of at least one solution. In particular, for n = 4, we obtain the existence of radial solutions.

Original language	English (US)
Pages (from-to)	275-281
Number of pages	7
Journal	Discrete and Continuous Dynamical Systems
Volume	7
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2001.7.275
State	Published - 2001

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Keywords

Conformally covariant equations
Higher order semilinear elliptic equations
Non-uniqueness
Variational method

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10.3934/dcds.2001.7.275

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keywords = "Conformally covariant equations, Higher order semilinear elliptic equations, Non-uniqueness, Variational method",

author = "Chang, {Sun Yung Alice} and Wenxiong Chen",

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AU - Chen, Wenxiong

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AB - In this paper, we study the higher order conformally covariant equation (- Δ)n/2 w = (n - 1)!enw x ∈ Rn for all even dimensions n. Let a = 1/|Sn| ∫Rn enw dx. We prove, for every 0 < a < 1, the existence of at least one solution. In particular, for n = 4, we obtain the existence of radial solutions.

KW - Conformally covariant equations

KW - Higher order semilinear elliptic equations

KW - Non-uniqueness

KW - Variational method

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A note on a class of higher order conformally covariant equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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