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

被引：0

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;

D O I：

暂无

中图分类号：

学科分类号：

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.

引用

共 50 条

[1] The Brezis-Nirenberg problem for systems involving divergence-form operators
Brown, Burton
Gluck, Mathew
Guingona, Vince
Hammons, Thomas
Parnes, Miriam
Pooley, Sean
Schweitzer, Avery
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2023, 30 (06):
[2] The Brezis-Nirenberg problem for fractional elliptic operators
Chen, Ko-Shin
Montenegro, Marcos
Yan, Xiaodong
MATHEMATISCHE NACHRICHTEN, 2017, 290 (10) : 1491 - 1511
[3] Brezis-Nirenberg problem and coron problem for polyharmonic operators
Ge, YX
ELLIPTIC AND PARABOLIC PROBLEMS: A SPECIAL TRIBUTE TO THE WORK OF HAIM BREZIS, 2005, 63 : 291 - 297
[4] The Brezis-Nirenberg problem for nonlocal systems
Faria, Luiz F. O.
Miyagaki, Olimpio H.
Pereira, Fabio R.
Squassina, Marco
Zhang, Chengxiang
ADVANCES IN NONLINEAR ANALYSIS, 2016, 5 (01) : 85 - 103
[5] Trilinear embedding for divergence-form operators with complex coefficients
Carbonaro, Andrea
Dragicevic, Oliver
Kovac, Vjekoslav
Skreb, Kristina Ana
ADVANCES IN MATHEMATICS, 2023, 431
[6] THE BREZIS-NIRENBERG PROBLEM FOR MIXED LOCAL AND NONLOCAL OPERATORS
Biagi, Stefano
BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, 2023, 14 (01) : 15 - 37
[7] The Brezis–Nirenberg type problem involving the square root of the Laplacian
Jinggang Tan
Calculus of Variations and Partial Differential Equations, 2011, 42 : 21 - 41
[8] On semigroup maximal operators associated with divergence-form operators with complex coefficients
Carbonaro, Andrea
Dragicevic, Oliver
JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 394 : 98 - 119
[9] On the Brezis-Nirenberg Problem
Schechter, M.
Zou, Wenming
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 197 (01) : 337 - 356
[10] CRITICAL BREZIS-NIRENBERG PROBLEM FOR NONLOCAL SYSTEMS
Faria, Luiz F. O.
Miyagaki, Olimpio H.
Pereira, Fabio R.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2017, 50 (01) : 333 - 355

← 1 2 3 4 5 →