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Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality
1. | Department of Mathematics, INS and MOE-LSC, Shanghai Jiao Tong University, Shanghai, China, China, China |
References:
[1] |
H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proceedings of the American Mathematical Society, 88 (1983), 486-490.
doi: 10.1090/S0002-9939-1983-0699419-3. |
[2] |
X. Chen and X. Zhen, Optimal summation interval and nonexistence of positive solutions to a discrete sytem, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 1720-1730.
doi: 10.1016/S0252-9602(14)60117-X. |
[3] |
W. Chen, C. Jin, C. Li and J. Lim, Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations, Discrete Contin. Dyn. Syst. 2005, suppl., (2005), 164-172. |
[4] |
W. Chen and C. Li, An integral system and the Lane-Emden conjecture, Discrete Contin. Dyn. Syst., 24 (2009), 1167-1184.
doi: 10.3934/dcds.2009.24.1167. |
[5] |
W. Chen and C. Li, Radial symmetry of solutions for some integral systems of Wolff type, Discrete Contin. Dyn. Syst., 30 (2011), 1083-1093.
doi: 10.3934/dcds.2011.30.1083. |
[6] |
W. Chen and C. Li, Regularity of solutions for a system of integral equations, Commun. Pure Appl. Anal., 4 (2005), 1-8.
doi: 10.3934/cpaa.2005.4.1. |
[7] |
W. Chen and C. Li, The best constant in a weighted Hardy-Littlewood-Sobolev inequality, Proc. Amer. Math. Soci., 136 (2008), 955-962.
doi: 10.1090/S0002-9939-07-09232-5. |
[8] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations, Communications in Partial Difference Equations, 30 (2005), 59-65.
doi: 10.1081/PDE-200044445. |
[9] |
W. Chen, C. Li and B. Ou, Qualitative properties of solutions for an integral equation, Discrete Contin. Dyn. Syst., 12 (2005), 347-354.
doi: 10.3934/dcds.2005.12.347. |
[10] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Communications on pure and applied mathematics, 59 (2006), 330-343.
doi: 10.1002/cpa.20116. |
[11] |
Z. Cheng and C. Li, An extended discrete Hardy-Littlewood-Sobolev inequality, Discrete Contin. Dyn. Syst., 34 (2014), 1951-1959.
doi: 10.3934/dcds.2014.34.1951. |
[12] |
G. Hardy, J. Littlewood and J. Pólya, Inequalities, $2^{nd}$ edition, Cambridge University Press, 1952. |
[13] |
C. Li and J. Villavert, An extention of the Hardy-Littlewood-Pólya inequality, Acta Math. Scientia, 31 (2011), 2285-2288.
doi: 10.1016/S0252-9602(11)60400-1. |
[14] |
E. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Annals of Math., 118 (1983), 349-374.
doi: 10.2307/2007032. |
show all references
References:
[1] |
H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proceedings of the American Mathematical Society, 88 (1983), 486-490.
doi: 10.1090/S0002-9939-1983-0699419-3. |
[2] |
X. Chen and X. Zhen, Optimal summation interval and nonexistence of positive solutions to a discrete sytem, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 1720-1730.
doi: 10.1016/S0252-9602(14)60117-X. |
[3] |
W. Chen, C. Jin, C. Li and J. Lim, Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations, Discrete Contin. Dyn. Syst. 2005, suppl., (2005), 164-172. |
[4] |
W. Chen and C. Li, An integral system and the Lane-Emden conjecture, Discrete Contin. Dyn. Syst., 24 (2009), 1167-1184.
doi: 10.3934/dcds.2009.24.1167. |
[5] |
W. Chen and C. Li, Radial symmetry of solutions for some integral systems of Wolff type, Discrete Contin. Dyn. Syst., 30 (2011), 1083-1093.
doi: 10.3934/dcds.2011.30.1083. |
[6] |
W. Chen and C. Li, Regularity of solutions for a system of integral equations, Commun. Pure Appl. Anal., 4 (2005), 1-8.
doi: 10.3934/cpaa.2005.4.1. |
[7] |
W. Chen and C. Li, The best constant in a weighted Hardy-Littlewood-Sobolev inequality, Proc. Amer. Math. Soci., 136 (2008), 955-962.
doi: 10.1090/S0002-9939-07-09232-5. |
[8] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations, Communications in Partial Difference Equations, 30 (2005), 59-65.
doi: 10.1081/PDE-200044445. |
[9] |
W. Chen, C. Li and B. Ou, Qualitative properties of solutions for an integral equation, Discrete Contin. Dyn. Syst., 12 (2005), 347-354.
doi: 10.3934/dcds.2005.12.347. |
[10] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Communications on pure and applied mathematics, 59 (2006), 330-343.
doi: 10.1002/cpa.20116. |
[11] |
Z. Cheng and C. Li, An extended discrete Hardy-Littlewood-Sobolev inequality, Discrete Contin. Dyn. Syst., 34 (2014), 1951-1959.
doi: 10.3934/dcds.2014.34.1951. |
[12] |
G. Hardy, J. Littlewood and J. Pólya, Inequalities, $2^{nd}$ edition, Cambridge University Press, 1952. |
[13] |
C. Li and J. Villavert, An extention of the Hardy-Littlewood-Pólya inequality, Acta Math. Scientia, 31 (2011), 2285-2288.
doi: 10.1016/S0252-9602(11)60400-1. |
[14] |
E. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Annals of Math., 118 (1983), 349-374.
doi: 10.2307/2007032. |
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