EXISTENCE THEOREMS FOR CRITICAL DEGENERATE EQUATIONS INVOLVING THE GRUSHIN OPERATORS

被引：0
|
作者：
Nguyen, Huong Thi Thu [1 ]
Nguyen, Tri Minh [2 ]
机构：
[1] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, Hanoi, Vietnam
[2] Vietnam Acad Sci & Technol, Inst Math, Hanoi, Vietnam
来源：
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2023年 / 38卷 / 01期
关键词：
Semilinear degenerate elliptic equations; Grushin operator; crit-ical exponent; critical point; BOUNDARY-VALUE-PROBLEMS; ELLIPTIC-EQUATIONS; CONVERGENCE;
D O I：
10.4134/CKMS.c220030
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we prove the existence of nontrivial weak solutions to the boundary value problem -G1u = u3 + f (x, y, u) in & omega;, u & GE; 0 in & omega;, u = 0 on partial differential & omega;, where & omega; is a bounded domain with smooth boundary in R3, G1 is a Grushin type operator, and f (x, y, u) is a lower order perturbation of u3 with f (x, y, 0) = 0. The nonlinearity involved is of critical exponent, which differs from the existing results in [11, 12].
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页码：137 / 151
页数：15
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