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Regularity, symmetry and uniqueness of positive solutions to a nonlinear elliptic system
1. | Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China, China, China |
References:
[1] |
W. Chen and C. Li, "Methods on Nolinear Elliptic Equation," AIMS Ser. Differ. Dyn. Syst., vol.4, AIMS, 2010. |
[2] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Comm Pure Appl Math, 59 (2006), 330-343.
doi: 10.1002/cpa.20116. |
[3] |
X. Chen and J. Yang, Regularity and symmetry of positive solutions of an integral system, Acta Math. Sci., 32B (2012), 1759-1780. |
[4] |
T. Kanna and M. Lakshmanan, Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations, Phys. Rev. Lett., 86 (2001), 5043-5046.
doi: 10.1103/PhysRevLett.86.5043. |
[5] |
M. Kwong, Uniqueness of positive solutions of $\Delta u-u+u^p=0$ in $\mathbbR^n$, Arch. Ration. Mech. Anal., 105 (1989), 243-266.
doi: 10.1007/BF00251502. |
[6] |
Y. Li, Remark on some conformlly invariant integral equations: The method of moving spheres, J. Eur. Math. Soc., 6 (2004), 153-180.
doi: 10.4171/JEMS/6. |
[7] |
C. Li and L. Ma, Uniqueness of positive bound states to Schrödinger systems with critical exponents, SIAM J. Math. Anal., 40 (2008), 1049-1057. |
[8] |
T. C. Lin and J. Wei, Ground state of N coupled nonlinear Schrödinger equations in $\mathbbR^n, n\leq 3$, Commun. Math. Phys., 255 (2005), 629-653.
doi: 10.1007/s00220-005-1313-x. |
[9] |
T. C. Lin and J. Wei, Spikes in two coupled nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 403-439.
doi: 10.1016/j.anihpc.2004.03.004. |
[10] |
L. Ma and D. Chen, Radial symmetry and monotonicity for an integral equation, J. Math. Anal. Appl., 342 (2008), 943-949.
doi: 10.1016/j.jmaa.2007.12.064. |
[11] |
L. Ma and D. Chen, Radial symmetry and uniqueness for positive solutions of a Schrödinger type systems, Mathematical and Computer Modelling, 49 (2009), 379-385.
doi: 10.1016/j.mcm.2008.06.010. |
[12] |
L. Ma and L. Zhao, Uniqueness of ground states of some coupled nonlinear Schrödinger systems and their application, J. Diffe. Equa., 245 (2008), 2551-2565.
doi: 10.1016/j.jde.2008.04008. |
[13] |
Y. Zhao and Y. Lei, Asymptotic behavior of positive solutions of a nonlinear integral system, Nonlinear Anal., 75 (2012), 1989-1999.
doi: 10.1016/j.na.2011.09.051. |
show all references
References:
[1] |
W. Chen and C. Li, "Methods on Nolinear Elliptic Equation," AIMS Ser. Differ. Dyn. Syst., vol.4, AIMS, 2010. |
[2] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Comm Pure Appl Math, 59 (2006), 330-343.
doi: 10.1002/cpa.20116. |
[3] |
X. Chen and J. Yang, Regularity and symmetry of positive solutions of an integral system, Acta Math. Sci., 32B (2012), 1759-1780. |
[4] |
T. Kanna and M. Lakshmanan, Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations, Phys. Rev. Lett., 86 (2001), 5043-5046.
doi: 10.1103/PhysRevLett.86.5043. |
[5] |
M. Kwong, Uniqueness of positive solutions of $\Delta u-u+u^p=0$ in $\mathbbR^n$, Arch. Ration. Mech. Anal., 105 (1989), 243-266.
doi: 10.1007/BF00251502. |
[6] |
Y. Li, Remark on some conformlly invariant integral equations: The method of moving spheres, J. Eur. Math. Soc., 6 (2004), 153-180.
doi: 10.4171/JEMS/6. |
[7] |
C. Li and L. Ma, Uniqueness of positive bound states to Schrödinger systems with critical exponents, SIAM J. Math. Anal., 40 (2008), 1049-1057. |
[8] |
T. C. Lin and J. Wei, Ground state of N coupled nonlinear Schrödinger equations in $\mathbbR^n, n\leq 3$, Commun. Math. Phys., 255 (2005), 629-653.
doi: 10.1007/s00220-005-1313-x. |
[9] |
T. C. Lin and J. Wei, Spikes in two coupled nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 403-439.
doi: 10.1016/j.anihpc.2004.03.004. |
[10] |
L. Ma and D. Chen, Radial symmetry and monotonicity for an integral equation, J. Math. Anal. Appl., 342 (2008), 943-949.
doi: 10.1016/j.jmaa.2007.12.064. |
[11] |
L. Ma and D. Chen, Radial symmetry and uniqueness for positive solutions of a Schrödinger type systems, Mathematical and Computer Modelling, 49 (2009), 379-385.
doi: 10.1016/j.mcm.2008.06.010. |
[12] |
L. Ma and L. Zhao, Uniqueness of ground states of some coupled nonlinear Schrödinger systems and their application, J. Diffe. Equa., 245 (2008), 2551-2565.
doi: 10.1016/j.jde.2008.04008. |
[13] |
Y. Zhao and Y. Lei, Asymptotic behavior of positive solutions of a nonlinear integral system, Nonlinear Anal., 75 (2012), 1989-1999.
doi: 10.1016/j.na.2011.09.051. |
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