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.

引用

页码：815 / 823

页数：9