Liouville-type theorem for a nonlinear sub-elliptic system involving Δλ-Laplacian and advection terms

被引：0

作者：

Duong, Anh Tuan ^{[1
]}

Quyet, Dao Trong ^{[2
]}

Biet, Nguyen Van ^{[3
]}

机构：

[1] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, Dai Co Viet 1, Hai Ba Trung, Ha Noi, Vietnam

[2] Acad Finance, Bac Tu Liem, Ha Noi, Vietnam

[3] Dept Educ & Training Phu Tho Prov, Viet Tri, Phu Tho, Vietnam

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2023年 / 25卷 / 02期

关键词：

Liouville-type theorem; advection terms; stable solutions; elliptic systems; POSITIVE SOLUTIONS; EQUATIONS; CLASSIFICATION; GRUSHIN;

D O I：

10.1007/s11784-023-01057-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the following system: {-w Delta(lambda)u - del(lambda)w. del(lambda)u -rho v(p) in R-N, -w Delta(lambda)v - del(lambda)w. del(lambda)v =rho v(q) where w, rho are nonnegative continuous functions satisfying some growth conditions at infinity and p, q > 1. Here, Delta(lambda) is the sub-elliptic operator introduced in [A.E. Kogoj and E. Lanconelli. Nonlinear Anal. 2012;75(12): 4637-4649] and is of the form Delta(lambda) = Sigma(N)(i=1) partial derivative x(i) (lambda(2)(i) partial derivative x(i)). Our purpose is to establish a Liouville-type theorem for the class of positive stable solutions of the system. On one hand, our result generalizes the result in Duong and Nguyen (Electron J Differ Equ Paper No. 108, 11 pp, 2017) from the equation to the system, and on the other hand, it extends that of Hu (NoDEA Nonlinear Differ Equ Appl 25(1):7, 2018) to the sub-elliptic case.

引用

页数：20

共 48 条

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