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A Liouville-type theorem for higher order elliptic systems
1. | Department of Mathematics, University of Connecticut, Storrs, CT 06269, United States, United States, United States |
References:
[1] |
J. Busca and R. Manásevich, A Liouville-type theorem for Lane-Emden systems, Indiana. J., 51 (2002), 37-51. |
[2] |
D. G. de Figueiredo and P. Felmer, A Liouville-type Theorem for elliptic systems, Ann. Sc. Norm. Sup. Pisa, 21(1994), 387-397. |
[3] |
C.-S. Lin, A classification of solutions of a conformally invariant fourth order equation in $\mathbb{R}^{N}$, Comment. Math. Helv., 73 (1998), 206-231.
doi: 10.1007/s000140050052. |
[4] |
J. Liu, Y. Guo and Y. Zhang, Liouville-type theorems for polyharmonic systems in $\mathbb{R}^{N}$, J. Differential Equations, 225 (2006), 685-709.
doi: 10.1016/j.jde.2005.10.016. |
[5] |
E. Mitidieri, A Rellich type identity and applications, Comm. P.D.E., 18 (1993), 125-151.
doi: 10.1080/03605309308820923. |
[6] |
E. Mitidieri, Non-existence of positive solutions of semilinear elliptic systems in $\mathbb{R}^{N}$., Diff. Int. Eq., 9 (1996), 465-479. |
[7] |
P. Poláčik, P. Quittner and Ph. Souplet, Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part I: Elliptic systems, Duke Math. J., 139 (2007), 411-619.
doi: 10.1215/S0012-7094-07-13935-8. |
[8] |
J. Serrin and H. Zou, Non-existence of positive solutions of semilinear elliptic systems, Discourses in Mathematics and its Applications, 3 (1994), 55-68. |
[9] |
J. Serrin and H. Zou, Non-existence of positive solutions of Lane-Emden systems, Diff. Int. Eq., 9 (1996), 635-653. |
[10] |
J. Serrin and H. Zou, Existence of positive solutions of Lane-Emden systems, Atti. Sem. mat. Fis. Univ. Modena, 46 (1998), 369-380. |
[11] |
P. Souplet, The proof of the Lane-Emden conjecture in four space dimensions, Adv. in Math., 221 (2009), 1409-1427.
doi: 10.1016/j.aim.2009.02.014. |
[12] |
M. A. Souto, Sobre a Existência de Soluç ões Positivas Para Sistemas Cooperativos Não Lineares, PhD thesis, Unicamp, 1992. |
[13] |
J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations, Math. Ann., 313 (1999), 207-228.
doi: 10.1007/s002080050258. |
[14] |
X. Yan, A Liouville Theorem for Higher order Elliptic system, J. Math. Anal. Appl., 387 (2012), 153-165.
doi: 10.1016/j.jmaa.2011.08.081. |
show all references
References:
[1] |
J. Busca and R. Manásevich, A Liouville-type theorem for Lane-Emden systems, Indiana. J., 51 (2002), 37-51. |
[2] |
D. G. de Figueiredo and P. Felmer, A Liouville-type Theorem for elliptic systems, Ann. Sc. Norm. Sup. Pisa, 21(1994), 387-397. |
[3] |
C.-S. Lin, A classification of solutions of a conformally invariant fourth order equation in $\mathbb{R}^{N}$, Comment. Math. Helv., 73 (1998), 206-231.
doi: 10.1007/s000140050052. |
[4] |
J. Liu, Y. Guo and Y. Zhang, Liouville-type theorems for polyharmonic systems in $\mathbb{R}^{N}$, J. Differential Equations, 225 (2006), 685-709.
doi: 10.1016/j.jde.2005.10.016. |
[5] |
E. Mitidieri, A Rellich type identity and applications, Comm. P.D.E., 18 (1993), 125-151.
doi: 10.1080/03605309308820923. |
[6] |
E. Mitidieri, Non-existence of positive solutions of semilinear elliptic systems in $\mathbb{R}^{N}$., Diff. Int. Eq., 9 (1996), 465-479. |
[7] |
P. Poláčik, P. Quittner and Ph. Souplet, Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part I: Elliptic systems, Duke Math. J., 139 (2007), 411-619.
doi: 10.1215/S0012-7094-07-13935-8. |
[8] |
J. Serrin and H. Zou, Non-existence of positive solutions of semilinear elliptic systems, Discourses in Mathematics and its Applications, 3 (1994), 55-68. |
[9] |
J. Serrin and H. Zou, Non-existence of positive solutions of Lane-Emden systems, Diff. Int. Eq., 9 (1996), 635-653. |
[10] |
J. Serrin and H. Zou, Existence of positive solutions of Lane-Emden systems, Atti. Sem. mat. Fis. Univ. Modena, 46 (1998), 369-380. |
[11] |
P. Souplet, The proof of the Lane-Emden conjecture in four space dimensions, Adv. in Math., 221 (2009), 1409-1427.
doi: 10.1016/j.aim.2009.02.014. |
[12] |
M. A. Souto, Sobre a Existência de Soluç ões Positivas Para Sistemas Cooperativos Não Lineares, PhD thesis, Unicamp, 1992. |
[13] |
J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations, Math. Ann., 313 (1999), 207-228.
doi: 10.1007/s002080050258. |
[14] |
X. Yan, A Liouville Theorem for Higher order Elliptic system, J. Math. Anal. Appl., 387 (2012), 153-165.
doi: 10.1016/j.jmaa.2011.08.081. |
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