On the nonexistence of stable solutions of sub-elliptic systems with negative exponents

被引：8

作者：

Anh Tuan Duong ^{[1
,2
]}

Do Lan ^{[3
]}

Phuong Quynh Le ^{[4
]}

Phuong Thao Nguyen ^{[4
]}

机构：

[1] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam

[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[3] Thuy Ioi Univ, Fac Comp Engn & Sci, Hanoi, Vietnam

[4] Hanoi Natl Univ Educ, Dept Math, Hanoi, Vietnam

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2019年 / 64卷 / 12期

关键词：

Liouville-type result; stable positive solutions; degenerate elliptic systems; negative exponents; LIOUVILLE THEOREMS; POSITIVE SOLUTIONS; EQUATION; INEQUALITIES;

D O I：

10.1080/17476933.2019.1574772

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the sub-elliptic system Delta(lambda)u = v(-p) in R-N, (1) Delta(lambda)v = u(-q) where p, q > 1 and Delta(lambda) is an operator of the form Delta(lambda) = Sigma(N)(i=1) partial derivative(xi) (lambda(2)(i)partial derivative(xi)). We establish some Liouville type results for bounded stable positive solutions of the system. As a consequence, we also obtain a nonexistence result for the scalar equation Lambda(lambda)u = u(-p), in R-N.

引用

页码：2117 / 2129

页数：13

共 22 条

[1] Liouville type theorem for nonlinear elliptic system involving Grushin operator [J].

Anh Tuan Duong ;

Quoc Hung Phan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 454 (02) :785-801

[2]

[Anonymous], 1996, DIFFER INTEGRAL EQU

[3]

[Anonymous], 1996, Differ. Integral Equ.

[4] Liouville theorems for stable Lane-Emden systems and biharmonic problems [J].

Cowan, Craig .

NONLINEARITY, 2013, 26 (08) :2357-2371

[5] Liouville-type theorems for elliptic inequalities involving the Δλ-Laplace operator [J].

Cung The Anh ;

Bui Kim My .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2016, 61 (07) :1002-1013

[6] Qualitative analysis of rupture solutions for a MEMS problem [J].

Davila, Juan ;

Wang, Kelei ;

Wei, Juncheng .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (01) :221-242

[7] Positive solutions of an elliptic equation with negative exponent: Stability and critical power [J].

Du, Yihong ;

Guo, Zongming .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (06) :2387-2414

[8]

Franchi B., 1984, REND SEM MAT U POLIT, P105

[9] Sub-harmonicity, monotonicity formula and finite Morse index solutions of an elliptic equation with negative exponent [J].

Guo ZongMing ;

Zhou Feng .

SCIENCE CHINA-MATHEMATICS, 2015, 58 (11) :2301-2316

[10] Finite Morse index steady states of van der Waals force driven thin film equations [J].

Guo, Zongming ;

Ma, Li .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 368 (02) :559-572

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