Liouville type theorems for stable solutions of p-Laplace equation in RN. (September 2017)

• Record Type: Journal Article
• Authors: Chen, Caisheng; Song, Hongxue; Yang, Hongwei
• Is Part Of: Nonlinear analysis. Volume 160(2017)
• Page Start: 44
• Page End: 52
• Publication Date: 2017-09
• Subjects: 35J60 -- 35B53 -- 35B33 -- 35B45; p-Laplace equation -- Stable solutions -- Liouville type theorems; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.05.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove the Liouville type theorems for stable solution of the p -Laplace equations (0.1) − Δ p u = f ( x ) e u, in R N and (0.2) Δ p u = f ( x ) u − q, in R N, where 2 ≤ p < N, q > 0 and the nonnegative function f ( x ) ∈ L l o c 1 ( R N ) such that f ( x ) ≥ c 0 | x | a as | x | ≥ R 0 with a > − p and some constants R 0, c 0 > 0 . The results hold true for 2 ≤ N < μ 0 ( p, a ) in (0.1) and for q > q c ( p, N, a ) in (0.2). Here μ 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 .