Existence and Non-existence of Solutions for Semilinear bi-Δγ-Laplace Equation

被引：2
|
作者：
Duong Trong Luyen [1 ]
Ha Tien Ngoan [2 ]
Phung Thi Kim Yen [3 ]
机构：
[1] Hoa Lu Univ, Dept Math, Ninh Binh City, Vietnam
[2] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam
[3] Ha Noi Univ Nat Resources & Environm, Dept Math, 41A Phu Dien, Hanoi, Vietnam
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2022年 / 45卷 / 02期
关键词：
Bi-Delta(gamma)-Laplace equations; Delta(gamma)-Laplace operator; Pohozaev's type identities; Nontrivial solutions; Weak solutions; Existence; Multiple solutions; HYPOELLIPTIC DIFFERENTIAL-OPERATORS; 4TH-ORDER ELLIPTIC EQUATION; BOUNDARY-VALUE-PROBLEMS; NONTRIVIAL SOLUTIONS; VECTOR-FIELDS; MULTIPLICITY;
D O I：
10.1007/s40840-021-01223-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study existence and non-existence of weak solutions for semilinear bi-Delta(gamma)-Laplace equation Delta(2)(gamma)u = f (x, u) in Omega, u = partial derivative(v)u = 0 on partial derivative Omega, where Omega is a bounded domain with smooth boundary in R-N (N >= 2), f (x, xi) is a Caratheodory function and Delta(gamma) is the subelliptic operator of the type Delta(gamma) := Sigma(N)(j=1) partial derivative(xj) (gamma(2)(j)partial derivative(xj)), partial derivative(xj) := partial derivative/partial derivative(xj), gamma = gamma(1), gamma(2), ... , gamma(N)), Delta(2)(gamma) := Delta(gamma) (Delta(gamma)).
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页码：819 / 838
页数：20
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