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Regularity estimates for nonlocal Schrödinger equations
Classification for positive solutions of degenerate elliptic system
1. | Department of Mathematics, Tsinghua University, Beijing 100084, China |
2. | Institute of Mathematics, Academy of Mathematics and Systems Science, Beijing 100190, China |
In this paper, by using the Alexandrov-Serrin method of moving plane combined with integral inequalities, we obtained the complete classification of positive solution for a class of degenerate elliptic system.
References:
[1] |
L. Almeida, L. Damascelli and Y. Ge,
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds, Annales Inst. H. Poincare, 19 (2002), 313-342.
doi: 10.1016/S0294-1449(01)00091-9. |
[2] |
G. Bianchi,
Non-existence of positive solutions to semilinear elliptic equations on $\mathbb{R^N}$ or $\mathbb{R}^N_+$ through the method of moving planes, Comm. in P.D. E., 22 (1997), 1671-1690.
doi: 10.1080/03605309708821315. |
[3] |
E. Colorado Heras and I. Peral Alonso,
Semilinear elliptic problems with mixed boundary conditions, J. Funct. Anal., 199 (2003), 468-507.
doi: 10.1016/S0022-1236(02)00101-5. |
[4] |
L. Damascelli and F. Gladiali,
Some nonexistence results for positive solutions of elliptic equations in unbounded domains, Rev. Mat. Iberoamericana, 20 (2004), 67-86.
|
[5] |
B. Gidas and J. Spruk,
Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure and Appl. Math., 34 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[6] |
Y. Guo and J. Liu,
Liouville Type Theorems for positive solutions of elliptic system in $\mathbb{R}^N$, Comm. Partial Differential Equations, 33 (2008), 263-284.
doi: 10.1080/03605300701257476. |
[7] |
G. Huang,
A liouville theorem of degenerate elliptic equation and its application, Discrete Contin. Dyn. Syst., 33 (2013), 4549-4566.
doi: 10.3934/dcds.2013.33.4549. |
[8] |
G. Huang and C. Li,
A Liouville theorem for high order degenerate elliptic equations, J. Differential Equations, 258 (2015), 1229-1251.
doi: 10.1016/j.jde.2014.10.017. |
[9] |
S. Terracini,
Symmetry properties of positives solutions to some elliptic equations with nonlinear boundary conditions, Diff. Int. Eq., 8 (1995), 1911-1922.
|
[10] |
S. Terracini,
On positive entire solutions to a class of equations with a singular coefficient and critical exponent, Adv. Diff. Eq., 1 (1996), 241-264.
|
show all references
References:
[1] |
L. Almeida, L. Damascelli and Y. Ge,
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds, Annales Inst. H. Poincare, 19 (2002), 313-342.
doi: 10.1016/S0294-1449(01)00091-9. |
[2] |
G. Bianchi,
Non-existence of positive solutions to semilinear elliptic equations on $\mathbb{R^N}$ or $\mathbb{R}^N_+$ through the method of moving planes, Comm. in P.D. E., 22 (1997), 1671-1690.
doi: 10.1080/03605309708821315. |
[3] |
E. Colorado Heras and I. Peral Alonso,
Semilinear elliptic problems with mixed boundary conditions, J. Funct. Anal., 199 (2003), 468-507.
doi: 10.1016/S0022-1236(02)00101-5. |
[4] |
L. Damascelli and F. Gladiali,
Some nonexistence results for positive solutions of elliptic equations in unbounded domains, Rev. Mat. Iberoamericana, 20 (2004), 67-86.
|
[5] |
B. Gidas and J. Spruk,
Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure and Appl. Math., 34 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[6] |
Y. Guo and J. Liu,
Liouville Type Theorems for positive solutions of elliptic system in $\mathbb{R}^N$, Comm. Partial Differential Equations, 33 (2008), 263-284.
doi: 10.1080/03605300701257476. |
[7] |
G. Huang,
A liouville theorem of degenerate elliptic equation and its application, Discrete Contin. Dyn. Syst., 33 (2013), 4549-4566.
doi: 10.3934/dcds.2013.33.4549. |
[8] |
G. Huang and C. Li,
A Liouville theorem for high order degenerate elliptic equations, J. Differential Equations, 258 (2015), 1229-1251.
doi: 10.1016/j.jde.2014.10.017. |
[9] |
S. Terracini,
Symmetry properties of positives solutions to some elliptic equations with nonlinear boundary conditions, Diff. Int. Eq., 8 (1995), 1911-1922.
|
[10] |
S. Terracini,
On positive entire solutions to a class of equations with a singular coefficient and critical exponent, Adv. Diff. Eq., 1 (1996), 241-264.
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