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Some properties of positive solutions for an integral system with the double weighted Riesz potentials
1. | College of Sciences, Hunan Agriculture University, Changsha Hunan 410128, China |
2. | Institute of Applied Physics and Computational Mathematics, P.O.Box 8009-28, Beijing 100088 |
3. | School of Mathematical Sciences, Xiamen University, Xiamen Fujian 361005, China |
References:
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W. Chen and C. Li, Methods on Nonlinear Elliptic Equations, AIMS Ser. Differ. Equ. Dyn. Syst., Vol. 4, 2010. |
[2] |
C. Jin and C. Li, Qualitative analysis of some systems of equations, Calc. Var. Partial Differential Equations, 26 (2006), 447-457.
doi: 10.1007/s00526-006-0013-5. |
[3] |
C. Jin and C. Li, Symmetry of solutions to some systems of integral equations, Proc. Amer. Math. Soc., 134 (2006), 1661-1670.
doi: 10.1090/S0002-9939-05-08411-X. |
[4] |
Y. Lei and C. Li, Sharp criteria of Liouville type for some nonlinear system, Discrete Contin. Dyn. Syst., 36 (2016), 3277-3315.
doi: 10.3934/dcds.2016.36.3277. |
[5] |
Y. Lei, C. Li and C. Ma, Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy-Littlewood-Sobolev system of integral equations, Calc. Var. Partial Differential Equations, 45 (2012), 43-61.
doi: 10.1007/s00526-011-0450-7. |
[6] |
Y. Lei and C. Ma, Asymptotic behavior for solutions of some integral equations, Comm. Pure Appl. Anal., 10 (2011), 193-207.
doi: 10.3934/cpaa.2011.10.193. |
[7] |
C. Li and J. Lim, The singularity analysis of solutions to some integral equations, Comm. Pure Appl. Anal., 6 (2007), 453-464.
doi: 10.3934/cpaa.2007.6.453. |
[8] |
C. Li and L. Ma, Uniqueness of positive bound states to schrödinger systems with critical expoents, SIAM J. Math. Anal., 40 (2008), 1049-1057.
doi: 10.1137/080712301. |
[9] |
E. H. Lieb and M. Loss, Analysis, 2nd edition, Graduate Studies in Mathematics, Vol.14, Amer. Math. Soc., Providence, R.I., 2001.
doi: 10.1090/gsm/014. |
[10] |
G. Lu and J. Zhu, Symmetry and regularity of extremals of an integral equation related to the Hardy-Sobolev inequality, Calc. Var. Partial Differential Equations, 42 (2011), 563-577.
doi: 10.1007/s00526-011-0398-7. |
[11] |
J. Xu, H. Wu and Z. Tan, Radial symmetry and asymptotic behaviors of positive solutions for certain nonlinear integral equations, J. Math. Anal. Appl., 427 (2015), 307-319.
doi: 10.1016/j.jmaa.2015.02.043. |
[12] |
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 Nonlinear Elliptic Equations, AIMS Ser. Differ. Equ. Dyn. Syst., Vol. 4, 2010. |
[2] |
C. Jin and C. Li, Qualitative analysis of some systems of equations, Calc. Var. Partial Differential Equations, 26 (2006), 447-457.
doi: 10.1007/s00526-006-0013-5. |
[3] |
C. Jin and C. Li, Symmetry of solutions to some systems of integral equations, Proc. Amer. Math. Soc., 134 (2006), 1661-1670.
doi: 10.1090/S0002-9939-05-08411-X. |
[4] |
Y. Lei and C. Li, Sharp criteria of Liouville type for some nonlinear system, Discrete Contin. Dyn. Syst., 36 (2016), 3277-3315.
doi: 10.3934/dcds.2016.36.3277. |
[5] |
Y. Lei, C. Li and C. Ma, Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy-Littlewood-Sobolev system of integral equations, Calc. Var. Partial Differential Equations, 45 (2012), 43-61.
doi: 10.1007/s00526-011-0450-7. |
[6] |
Y. Lei and C. Ma, Asymptotic behavior for solutions of some integral equations, Comm. Pure Appl. Anal., 10 (2011), 193-207.
doi: 10.3934/cpaa.2011.10.193. |
[7] |
C. Li and J. Lim, The singularity analysis of solutions to some integral equations, Comm. Pure Appl. Anal., 6 (2007), 453-464.
doi: 10.3934/cpaa.2007.6.453. |
[8] |
C. Li and L. Ma, Uniqueness of positive bound states to schrödinger systems with critical expoents, SIAM J. Math. Anal., 40 (2008), 1049-1057.
doi: 10.1137/080712301. |
[9] |
E. H. Lieb and M. Loss, Analysis, 2nd edition, Graduate Studies in Mathematics, Vol.14, Amer. Math. Soc., Providence, R.I., 2001.
doi: 10.1090/gsm/014. |
[10] |
G. Lu and J. Zhu, Symmetry and regularity of extremals of an integral equation related to the Hardy-Sobolev inequality, Calc. Var. Partial Differential Equations, 42 (2011), 563-577.
doi: 10.1007/s00526-011-0398-7. |
[11] |
J. Xu, H. Wu and Z. Tan, Radial symmetry and asymptotic behaviors of positive solutions for certain nonlinear integral equations, J. Math. Anal. Appl., 427 (2015), 307-319.
doi: 10.1016/j.jmaa.2015.02.043. |
[12] |
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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