Liouville type theorems for stable solutions of p-Laplace equation in RN

被引：28

作者：

Chen, Caisheng ^{[1
]}

Song, Hongxue ^{[1
,2
]}

Yang, Hongwei ^{[3
]}

机构：

[1] Hohai Univ, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China

[2] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Jiangsu, Peoples R China

[3] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 160卷

关键词：

p-Laplace equation; Stable solutions; Liouville type theorems; DEGENERATE ELLIPTIC-EQUATIONS; MORSE-INDEX SOLUTIONS; POSITIVE SOLUTIONS; NEGATIVE EXPONENT; DELTA-U; REGULARITY; CLASSIFICATION; STABILITY; E(U);

D O I：

10.1016/j.na.2017.05.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the Liouville type theorems for stable solution of the p-Laplace equation -Delta(p)u = f(x)e(u), in R-N (0.1) and Delta(p)u = f(x)u(-q), in R-N, (0.2) where 2 <= p < N, q > 0 and the nonnegative function f(x) is an element of L-loc(1)(R-N) such that f (x) > c(0)broken vertical bar x vertical bar(a) as Ixl > R-0 with a > -p and some constants R-0, c(0) > 0. The results hold true for 2 <= N < mu(0)(p, a) in (0.1) and for q > q(c)(p, N, a) in (0.2). Here mu(0) and q(c) are new exponents, which are always large than the classical critical ones and depend on the parameters p, a and N. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：44 / 52

页数：9

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