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.
引用
收藏
页码：1051 / 1063
页数：13
相关论文
共 17 条
  • [1] Chen H., Chen H.-G., Li J.-N., Estimates of Dirichlet eigenvalues for degenerate -Laplace operator, Calc. Var. Partial Differ. Equ, 59, 4, (2020)
  • [2] Jerison D.S., The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. II, J. Funct. Anal, 43, pp. 224-257, (1981)
  • [3] Jerison D., Lee J.M., The Yamabe problem on CR manifolds, J. Diff. Geom, 25, pp. 167-197, (1987)
  • [4] Luyen D.T., Tri N.M., On the existence of multiple solutions to boundary value problems for semilinear elliptic degenerate operators, Complex Var. Elliptic Equ, 64, 6, pp. 1050-1066, (2019)
  • [5] Nga N.Q., Tri N.M., Tuan D.A., Existence and nonexistence of nontrivial solutions for degenerate elliptic equations in a solid torus, J. Elliptic Parabol. Equ, 9, 1, pp. 401-417, (2023)
  • [6] Thuy P.T., Tri N.M., Nontrivial solutions to boundary value problems for semilinear strongly degenerate elliptic differential equations, NoDEA Nonlinear Differ. Equ. Appl, 19, 3, pp. 279-298, (2012)
  • [7] Tri N.M., On Grushin’s equation, Math. Notes, 63, 1, pp. 84-93, (1998)
  • [8] Nguyen M.T., Critical Sobolev exponent for degenerate elliptic operators, Acta Math. Vietnam, 23, 1, pp. 83-94, (1998)
  • [9] Tri N.M., Semilinear Degenerate Elliptic Differential Equations, Local and Global Theories, (2010)
  • [10] Tri N.M., Recent Progress in the Theory of Semilinear Equations Involving Degenerate Elliptic Differential Operators, (2014)
12