EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR A CLASS OF HAMILTONIAN STRONGLY DEGENERATE ELLIPTIC SYSTEM

被引：0

作者：

Nguyen Viet Tuan ^{[1
]}

机构：

[1] Sao Do Univ, Fac Basic Sci, Chi Linh, Hai Duong, Vietnam

来源：

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2023年 / 38卷 / 03期

关键词：

Hamiltonian elliptic system; variational methods; strongly degenerate; existence and nonexistence; DELTA(LAMBDA)-LAPLACE EQUATIONS;

D O I：

10.4134/CKMS.c220080

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth {-Delta(lambda)u - mu v = vertical bar v vertical bar(p-1)v in Omega, -Delta(lambda)v - mu u = vertical bar u vertical bar(q-1)u in Omega, u = v = 0 on partial derivative Omega, where p, q > 1 and Omega is a smooth bounded domain in R-N, N >= 3. Here Delta(lambda) is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

引用

页码：741 / 754

页数：14

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