The Brezis–Nirenberg problem for systems involving divergence-form operators

被引：0
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作者：
Burton Brown
Mathew Gluck
Vince Guingona
Thomas Hammons
Miriam Parnes
Sean Pooley
Avery Schweitzer
机构：
[1] American Public University,
[2] Human Resources office,undefined
[3] Southern Illinois University,undefined
[4] Towson University,undefined
[5] University of Illinois,undefined
[6] Chicago,undefined
[7] The University of Mississippi,undefined
[8] North Carolina State University,undefined
来源：
Nonlinear Differential Equations and Applications NoDEA | 2023年 / 30卷
关键词：
Semilinear elliptic system; Critical exponent; Positive solution; 35J47; 35J61;
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摘要：
We study a system of nonlinear elliptic partial differential equations involving divergence-form operators. The problem under consideration is a natural generalization of the classical Brezis–Nirenberg problem. We find conditions on the domain, the coupling coefficients and the coefficients of the differential operator under which positive solutions are guaranteed to exist and conditions on these objects under which no positive solution exists.
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