Two nontrivial solutions of boundary-value problems for semilinear Δ γ -differential equations

被引：15
|
作者：
Luyen, D. T. [1 ]
机构：
[1] Hoa Lu Univ, Dept Math, Ninh Nhat Ninh Binh City, Vietnam
来源：
MATHEMATICAL NOTES | 2017年 / 101卷 / 5-6期
关键词：
Semilinear degenerate elliptic equations; critical points; two solutions; multiple solutions; HEISENBERG-GROUP; EXISTENCE;
D O I：
10.1134/S0001434617050078
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the existence of multiple solutions for the boundary-value problem Delta(gamma)u + f(x,u) = 0 in Omega, u = 0 on partial derivative Omega where Omega is a bounded domain with smooth boundary in R-N (N >= 2) and Delta(gamma) is the subelliptic operator of the type Delta gamma u = Sigma xj (gamma j2xju), xju=u/xj; gamma =(gamma 1,gamma 2,...,gamma N). We use the three critical point theorem.
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页码：815 / 823
页数：9
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