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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., (2010).
|
[2] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation,, Comm Pure Appl Math, 59 (2006), 330.
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.
|
[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.
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.
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.
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.
|
[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.
doi: 10.1007/s00220-005-1313-x. |
[9] |
T. C. Lin and J. Wei, Spikes in two coupled nonlinear Schrödinger equations,, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, 22 (2005), 403.
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.
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.
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.
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.
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., (2010).
|
[2] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation,, Comm Pure Appl Math, 59 (2006), 330.
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.
|
[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.
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.
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.
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.
|
[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.
doi: 10.1007/s00220-005-1313-x. |
[9] |
T. C. Lin and J. Wei, Spikes in two coupled nonlinear Schrödinger equations,, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, 22 (2005), 403.
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.
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.
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.
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.
doi: 10.1016/j.na.2011.09.051. |
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