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A Liouville-type theorem for higher order elliptic systems of Hé non-Lane-Emden type
1. | Department of Mathematics, University of Connecticut, Storrs, CT 06269 |
References:
[1] |
F. Arthur, X. Yan and M. Zhao, A Liouville theorem for higher order elliptic system, Discrete Contin. Dyn. Syst., 34 (2014), 2513-2533.
doi: 10.3934/dcds.2014.34.3317. |
[2] |
J. Busca and R. Manásevich, A Liouville-type theorem for Lane-Emden systems, Indiana. J., 51 (2002), 37-51. |
[3] |
C. Cowan, A Liouville theorem for a fourth order Hé non equation, Adv. Nonlinear Stud., 14 (2014), 767-776. |
[4] |
M. Fazly, Liouville theorems for the polyharmonic Hé non-Lane-Emden system, Methods. Appl. Anal., 21 (2014), 265-281.
doi: 10.4310/MAA.2014.v21.n2.a5. |
[5] |
M. Fazly and N. Ghoussoub, On the Hénon-Lane-Emden conjecture, Discrete Contin. Dyn. Syst., 34 (2014), 2513-2533.
doi: 10.3934/dcds.2014.34.2513. |
[6] |
P. Felmer and D. G. de Figueiredo, A Liouville-type Theorem for elliptic systems, Ann. Sc. Norm. Sup. Pisa, XXI (1994), 387-397. |
[7] |
C.-S. Lin, A classification of solutions of a,conformally invariant fourth order equation in $\mathbbR^n$, Comment. Math. Helv., 73 (1998), 206-231.
doi: 10.1007/s000140050052. |
[8] |
J. Liu, Y. Guo and Y. Zhang, Liouville-type theorems for polyharmonic systems in $\mathbbR^n$, J. Differential Equations, 225 (2006), 685-709.
doi: 10.1016/j.jde.2005.10.016. |
[9] |
E. Mitidieri, A Rellich type identity and applications, Comm. P.D.E., 18 (1993), 125-151.
doi: 10.1080/03605309308820923. |
[10] |
E. Mitidieri, Non-existence of positive solutions of semilinear elliptic systems in $\mathbbR^n$, Diff. Int. Eq., 9 (1996), 465-479. |
[11] |
Q. H. Phan, Liouville-type theorems and bounds of solutions for Hardy-Hénon equations, Adv. Differential Equations, 17 (2012), 605-634. |
[12] |
Q. H. Phan and Ph. Souplet, Liouville-type theorems and bounds of solutions of Hardy-Hénon equaions, J. Diff. Equ., 252 (2012), 2544-2562.
doi: 10.1016/j.jde.2011.09.022. |
[13] |
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), 555-579.
doi: 10.1215/S0012-7094-07-13935-8. |
[14] |
J. Serrin and H. Zou, Non-existence of positive solutions of semilinear elliptic systems, Discourses in Mathematics and its Applications, 3 (1994), 55-68. |
[15] |
J. Serrin and H. Zou, Non-existence of positive solutions of Lane-Emden systems, Diff. Int. Eq., 9 (1996), 635-653. |
[16] |
J. Serrin and H. Zou, Existence of positive solutions of Lane-Emden systems, Atti Sem. mat. Fis. Univ. Modena, 46 suppl (1998), 369-380. |
[17] |
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. |
[18] |
M. A. Souto, Sobre a existência de soluçōes positivas para sistemas cooperativos nāo lineares, PhD thesis, Unicamp (1992). |
[19] |
J. Villavert, Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality, J. Differential Equations, 258 (2015), 1685-1714.
doi: 10.1016/j.jde.2014.11.011. |
[20] |
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] |
F. Arthur, X. Yan and M. Zhao, A Liouville theorem for higher order elliptic system, Discrete Contin. Dyn. Syst., 34 (2014), 2513-2533.
doi: 10.3934/dcds.2014.34.3317. |
[2] |
J. Busca and R. Manásevich, A Liouville-type theorem for Lane-Emden systems, Indiana. J., 51 (2002), 37-51. |
[3] |
C. Cowan, A Liouville theorem for a fourth order Hé non equation, Adv. Nonlinear Stud., 14 (2014), 767-776. |
[4] |
M. Fazly, Liouville theorems for the polyharmonic Hé non-Lane-Emden system, Methods. Appl. Anal., 21 (2014), 265-281.
doi: 10.4310/MAA.2014.v21.n2.a5. |
[5] |
M. Fazly and N. Ghoussoub, On the Hénon-Lane-Emden conjecture, Discrete Contin. Dyn. Syst., 34 (2014), 2513-2533.
doi: 10.3934/dcds.2014.34.2513. |
[6] |
P. Felmer and D. G. de Figueiredo, A Liouville-type Theorem for elliptic systems, Ann. Sc. Norm. Sup. Pisa, XXI (1994), 387-397. |
[7] |
C.-S. Lin, A classification of solutions of a,conformally invariant fourth order equation in $\mathbbR^n$, Comment. Math. Helv., 73 (1998), 206-231.
doi: 10.1007/s000140050052. |
[8] |
J. Liu, Y. Guo and Y. Zhang, Liouville-type theorems for polyharmonic systems in $\mathbbR^n$, J. Differential Equations, 225 (2006), 685-709.
doi: 10.1016/j.jde.2005.10.016. |
[9] |
E. Mitidieri, A Rellich type identity and applications, Comm. P.D.E., 18 (1993), 125-151.
doi: 10.1080/03605309308820923. |
[10] |
E. Mitidieri, Non-existence of positive solutions of semilinear elliptic systems in $\mathbbR^n$, Diff. Int. Eq., 9 (1996), 465-479. |
[11] |
Q. H. Phan, Liouville-type theorems and bounds of solutions for Hardy-Hénon equations, Adv. Differential Equations, 17 (2012), 605-634. |
[12] |
Q. H. Phan and Ph. Souplet, Liouville-type theorems and bounds of solutions of Hardy-Hénon equaions, J. Diff. Equ., 252 (2012), 2544-2562.
doi: 10.1016/j.jde.2011.09.022. |
[13] |
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), 555-579.
doi: 10.1215/S0012-7094-07-13935-8. |
[14] |
J. Serrin and H. Zou, Non-existence of positive solutions of semilinear elliptic systems, Discourses in Mathematics and its Applications, 3 (1994), 55-68. |
[15] |
J. Serrin and H. Zou, Non-existence of positive solutions of Lane-Emden systems, Diff. Int. Eq., 9 (1996), 635-653. |
[16] |
J. Serrin and H. Zou, Existence of positive solutions of Lane-Emden systems, Atti Sem. mat. Fis. Univ. Modena, 46 suppl (1998), 369-380. |
[17] |
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. |
[18] |
M. A. Souto, Sobre a existência de soluçōes positivas para sistemas cooperativos nāo lineares, PhD thesis, Unicamp (1992). |
[19] |
J. Villavert, Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality, J. Differential Equations, 258 (2015), 1685-1714.
doi: 10.1016/j.jde.2014.11.011. |
[20] |
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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