HIGHER ORDER CONFORMALLY INVARIANT EQUATIONS IN R3 WITH PRESCRIBED VOLUME

被引：2

作者：

Hyder, Ali ^{[1
]}

Wei, Juncheng ^{[1
]}

机构：

[1] Univ British Columbia, Dept Math, 1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2019年 / 18卷 / 05期

基金：

瑞士国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Conformal metric; Q-curvature; large volume; negative exponent; higher order elliptic equation; NONLINEAR BIHARMONIC-EQUATIONS; 4TH-ORDER EQUATION; INTEGRAL-EQUATIONS; METRICS;

D O I：

10.3934/cpaa.2019123

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the following conformally invariant polyharmonic equation Delta(m)u = -u(3+2m/3-2m) in R-3, u > 0, with m = 2, 3. We prove the existence of positive smooth radial solutions with prescribed volume integral(R3) u(6/3-2m) dx. We show that the set of all possible values of the volume is a bounded interval (0,Lambda*] for m = 2, and it is (0,infinity) for m = 3. This is in sharp contrast to m = 1 case in which the volume integral(R3) u(6/3-2m) dx is a fixed value.

引用

页码：2781 / 2788

页数：8

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