Classification of radial solutions to equations related to Caffarelli-Kohn-Nirenberg inequalities

被引：5

作者：

Villavert, John ^{[1
]}

机构：

[1] Univ Texas, Edinburg, TX 78539 USA

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2020年 / 199卷 / 01期

关键词：

Asymptotic; Caffarelli-Kohn-Nirenberg inequalities; Classification of solutions; Henon-Lane-Emden equation; Liouville theorem; Hardy-Sobolev inequality; Phase plane; Radial solution; LIOUVILLE-TYPE THEOREMS; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; SUPERLINEAR PROBLEMS; ASYMPTOTIC-BEHAVIOR; LOCAL BEHAVIOR; SINGULARITY; EXISTENCE; CONSTANT; SYMMETRY;

D O I：

10.1007/s10231-019-00879-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article studies the qualitative and quantitative properties of radial solutions to an elliptic equation related to the Euler-Lagrange equations for certain sharp Caffarelli-Kohn-Nirenberg inequalities. Namely, we examine the equation -div(vertical bar x vertical bar(a) Du) = vertical bar x vertical bar(b)u(p), u > 0, in R-N, where p > 1, N >= 2, N - 2+ a >= 0 and b > - N. The main results establish the properties of radially symmetric solutions including existence, uniqueness, and classification results as well as results on the asymptotic and intersecting behaviour of such solutions.

引用

页码：299 / 315

页数：17

共 41 条

[1]

[Anonymous], 1980, NONLINEAR PARTIAL DI

[2]

[Anonymous], 2001, T MAT I STEKLOVA

[3]

AUBIN T, 1976, J MATH PURE APPL, V55, P269

[4] Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations [J].