Nontrivial Solutions of the Dirichlet Problems for Semilinear Degenerate Elliptic Equations

被引：0
|
作者：
Luyen, D. T. [1 ]
Tri, N. M. [2 ]
Tuan, D. A. [3 ]
机构：
[1] Hoa Lu Univ, Dept Math, Ninh Binh, Vietnam
[2] Vietnam Acad Sci & Technol, Inst Math, Cau Giay 10307, Hanoi, Vietnam
[3] Vietnam Natl Univ, Univ Sci, Hanoi, Vietnam
来源：
MATHEMATICAL NOTES | 2024年 / 116卷 / 5-6期
关键词：
boundary value problem; critical growth; critical value; nontrivial solution; embedding theorem; Pohozaev's type identity; EXISTENCE;
D O I：
10.1134/S0001434624110178
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we study the existence of nontrivial weak solutions of the boundary value problem -partial derivative(2)u/partial derivative x(2)-|x|(2k) partial derivative(2)u/partial derivative y(2)=f(x, y, u)in Omega,u=0on partial derivative Omega, where Omega is a bounded domain with smooth boundary in R-2,Omega boolean AND{x=0} =& empty;,k>0,f(x, y,0) = 0.
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页码：1051 / 1063
页数：13
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