EXISTENCE AND NON-EXISTENCE OF SOLUTIONS OF THE MEAN FIELD EQUATIONS ON FLAT TORI

被引：3

作者：

Chen, Zhijie ^{[1
]}

Kuo, Ting-Jung ^{[2
,3
]}

Lin, Chang-Shou ^{[4
]}

机构：

[1] Tsinghua Univ, Yau Math Sci Ctr, Dept Math Sci, Beijing 100084, Peoples R China

[2] Natl Taiwan Univ, TIMS, Taipei 10617, Taiwan

[3] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan

[4] Natl Taiwan Univ, CASTS, TIMS, Taipei 10617, Taiwan

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 09期

关键词：

D O I：

10.1090/proc/13543

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence or non-existence of solutions of the mean field equation (1.1) with n = 1 or n = 2 for a rectangular torus E. It is interesting to see that the results depend on the location of the half period omega k/2.

引用

页码：3989 / 3996

页数：8

共 50 条

[1] Non-existence of solutions for a mean field equation on flat tori at critical parameter 16π
Chen, Zhijie
Kuo, Ting-Jung
Lin, Chang-Shou
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2019, 27 (08) : 1737 - 1755
[2] A priori estimates, existence and non-existence of positive solutions of generalized mean curvature equations
Dai, Qiuyi
Gu, Yonggeng
Zhu, Jiuyi
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (18) : 7126 - 7136
[3] On the non-existence of regular stationary solutions of relativistic field equations
Einstein, A
Pauli, W
[J]. ANNALS OF MATHEMATICS, 1943, 44 : 131 - 137
[4] Existence and non-existence of global solutions for uniformly parabolic equations
Rodrigo Meneses
Alexander Quaas
[J]. Journal of Evolution Equations, 2012, 12 : 943 - 955
[5] Existence and non-existence of global solutions for uniformly parabolic equations
Meneses, Rodrigo
Quaas, Alexander
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2012, 12 (04) : 943 - 955
[6] On the existence or non-existence of solutions for certain backward stochastic differential equations
Lepeltier, JP
San Martín, J
[J]. BERNOULLI, 2002, 8 (01) : 123 - 137
[7] Existence and non-existence of solutions to elliptic equations with a general convection term
Alarcon, Salomon
Garcia-Melian, Jorge
Quaas, Alexander
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2014, 144 (02) : 225 - 239
[8] Existence and non-existence of solutions for a class of Monge-Ampere equations
Zhang, Zhitao
Wang, Kelei
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (07) : 2849 - 2875
[9] Existence and non-existence of global solutions for a class of non-linear wave equations
Chen, GW
Yang, ZJ
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2000, 23 (07) : 615 - 631
[10] Existence and non-existence of solutions for Timoshenko-type equations with variable exponents
Antontsev, Stanislav N.
Ferreira, Jorge
Piskin, Erhan
Siqueira Cordeiro, Sebastiao Martins
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 61

← 1 2 3 4 5 →