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Eigenvalues for a nonlocal pseudo $p-$Laplacian
Classification of positive solutions to a Lane-Emden type integral system with negative exponents
1. | School of Statistics, Xi'an University of Finance and Economics, Xi'an, Shaanxi, 710100 |
2. | School of National Fiscal Development, Central University of Finance and Economics, Beijing 100081, China |
3. | School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX 78539, United States |
References:
[1] |
G. Caristi, L. D'Ambrosio and E. Mitidieri, Representation formulae for solutions to some classes of higher order systems and related Liouville theorems,, Milan J. Math., 76 (2008), 27.
doi: 10.1007/s00032-008-0090-3. |
[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] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations,, Comm. Partial Differential Equations, 30 (2005), 59.
doi: 10.1081/PDE-200044445. |
[4] |
W. Chen, C. Li and B. Ou, Qualitative properties of solutions for an integral equation,, Discrete Contin. Dyn. Syst, 12 (2005), 347.
|
[5] |
W. Chen and C. Li, An integral system and the Lane-Emdem conjecture,, Discrete Contin. Dyn. Syst., 24 (2009), 1167.
doi: 10.3934/dcds.2009.24.1167. |
[6] |
J. Dou, Liouville type theorems for the system of integral equations,, Appl. Math. Comput., 217 (2010), 2586.
doi: 10.1016/j.amc.2010.07.071. |
[7] |
J. Dou and M. Zhu, Sharp Hardy-Littlewood-Sobolev inequality on the upper half space,, Int. Math. Res. Not., 3 (2015), 651.
|
[8] |
J. Dou and M. Zhu, Reversed Hardy-Littlewood-Sobolev inequality,, Int. Math. Res. Not., 19 (2015), 9696.
doi: 10.1093/imrn/rnu241. |
[9] |
M. Ghergu, Lane-Emden systems with negative exponents,, J. Funct. Anal., 258 (2010), 3295.
doi: 10.1016/j.jfa.2010.02.003. |
[10] |
Y. Han and M. Zhu, Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications., J. Differential Equations, 260 (2016), 1.
doi: 10.1016/j.jde.2015.06.032. |
[11] |
F. Hang, On the integral systems related to Hardy-Littlewood-Sobolev inequality,, Math. Res. Lett., 14 (2007), 373.
doi: 10.4310/MRL.2007.v14.n3.a2. |
[12] |
Y. Lei, On the integral systems with negative exponents,, Discrete Contin. Dyn. Syst., 35 (2015), 1039.
doi: 10.3934/dcds.2015.35.1039. |
[13] |
Y. Lei and C. Li, Sharp criteria of Liouville type for some nonlinear systems,, Discrete Contin. Dyn. Syst., 36 (2016), 3277.
doi: 10.3934/dcds.2016.36.3277. |
[14] |
C. Li and J. Villavert, A degree theory framework for semilinear elliptic systems,, Proc. Amer. Math. Soc., 144 (2016), 3731.
doi: 10.1090/proc/13166. |
[15] |
C. Li and J. Villavert, Existence of positive solutions to semilinear elliptic systems with supercritical growth,, Comm. Partial Differential Equations, 41 (2016), 1029.
doi: 10.1080/03605302.2016.1190376. |
[16] |
Y. Y. Li and M. Zhu, Uniqueness theorems through the method of moving spheres,, Duke Math. J., 80 (1995), 383.
doi: 10.1215/S0012-7094-95-08016-8. |
[17] |
Y. Y. Li and L. Zhang, Liouville type theorems and Harnack type inequalities for semilinear elliptic equations,, J. Anal. Math., 90 (2003), 27.
doi: 10.1007/BF02786551. |
[18] |
Y. Y. Li, Remark on some conformally invariant integral equations: The method of moving spheres,, J. Eur. Math. Soc. (JEMS), 6 (2004), 153.
|
[19] |
E. H. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities,, Ann. of Math., 118 (1983), 349.
doi: 10.2307/2007032. |
[20] |
J. Liu, Y. Guo and Y. Zhang, Existence of positive entire solutions for polyharmonic equations and systems,, J. Partial Differential Equations, 19 (2006), 256.
|
[21] |
L. Ma and D. Chen, A Liouville type theorem for an integral system,, Commun. Pure Appl. Anal., 5 (2006), 855.
doi: 10.3934/cpaa.2006.5.855. |
[22] |
Q. A. Ngô and V. H. Nguyen, Sharp Reversed Hardy-Littlewood-Sobolev inequality on $\mathbfR^n$,, Israel J. Math., (). Google Scholar |
[23] |
J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations,, Math. Ann., 313 (1999), 207.
doi: 10.1007/s002080050258. |
[24] |
X. Xu, Uniqueness theorem for integral equations and its application,, J. Funct. Anal., 247 (2007), 95.
doi: 10.1016/j.jfa.2007.03.005. |
[25] |
Z. Zhang, Positive solutions of Lane-Emden systems with negative exponents: Existence, boundary behavior and uniqueness,, Nonlinear Anal., 74 (2011), 5544.
doi: 10.1016/j.na.2011.05.038. |
show all references
References:
[1] |
G. Caristi, L. D'Ambrosio and E. Mitidieri, Representation formulae for solutions to some classes of higher order systems and related Liouville theorems,, Milan J. Math., 76 (2008), 27.
doi: 10.1007/s00032-008-0090-3. |
[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] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations,, Comm. Partial Differential Equations, 30 (2005), 59.
doi: 10.1081/PDE-200044445. |
[4] |
W. Chen, C. Li and B. Ou, Qualitative properties of solutions for an integral equation,, Discrete Contin. Dyn. Syst, 12 (2005), 347.
|
[5] |
W. Chen and C. Li, An integral system and the Lane-Emdem conjecture,, Discrete Contin. Dyn. Syst., 24 (2009), 1167.
doi: 10.3934/dcds.2009.24.1167. |
[6] |
J. Dou, Liouville type theorems for the system of integral equations,, Appl. Math. Comput., 217 (2010), 2586.
doi: 10.1016/j.amc.2010.07.071. |
[7] |
J. Dou and M. Zhu, Sharp Hardy-Littlewood-Sobolev inequality on the upper half space,, Int. Math. Res. Not., 3 (2015), 651.
|
[8] |
J. Dou and M. Zhu, Reversed Hardy-Littlewood-Sobolev inequality,, Int. Math. Res. Not., 19 (2015), 9696.
doi: 10.1093/imrn/rnu241. |
[9] |
M. Ghergu, Lane-Emden systems with negative exponents,, J. Funct. Anal., 258 (2010), 3295.
doi: 10.1016/j.jfa.2010.02.003. |
[10] |
Y. Han and M. Zhu, Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds and applications., J. Differential Equations, 260 (2016), 1.
doi: 10.1016/j.jde.2015.06.032. |
[11] |
F. Hang, On the integral systems related to Hardy-Littlewood-Sobolev inequality,, Math. Res. Lett., 14 (2007), 373.
doi: 10.4310/MRL.2007.v14.n3.a2. |
[12] |
Y. Lei, On the integral systems with negative exponents,, Discrete Contin. Dyn. Syst., 35 (2015), 1039.
doi: 10.3934/dcds.2015.35.1039. |
[13] |
Y. Lei and C. Li, Sharp criteria of Liouville type for some nonlinear systems,, Discrete Contin. Dyn. Syst., 36 (2016), 3277.
doi: 10.3934/dcds.2016.36.3277. |
[14] |
C. Li and J. Villavert, A degree theory framework for semilinear elliptic systems,, Proc. Amer. Math. Soc., 144 (2016), 3731.
doi: 10.1090/proc/13166. |
[15] |
C. Li and J. Villavert, Existence of positive solutions to semilinear elliptic systems with supercritical growth,, Comm. Partial Differential Equations, 41 (2016), 1029.
doi: 10.1080/03605302.2016.1190376. |
[16] |
Y. Y. Li and M. Zhu, Uniqueness theorems through the method of moving spheres,, Duke Math. J., 80 (1995), 383.
doi: 10.1215/S0012-7094-95-08016-8. |
[17] |
Y. Y. Li and L. Zhang, Liouville type theorems and Harnack type inequalities for semilinear elliptic equations,, J. Anal. Math., 90 (2003), 27.
doi: 10.1007/BF02786551. |
[18] |
Y. Y. Li, Remark on some conformally invariant integral equations: The method of moving spheres,, J. Eur. Math. Soc. (JEMS), 6 (2004), 153.
|
[19] |
E. H. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities,, Ann. of Math., 118 (1983), 349.
doi: 10.2307/2007032. |
[20] |
J. Liu, Y. Guo and Y. Zhang, Existence of positive entire solutions for polyharmonic equations and systems,, J. Partial Differential Equations, 19 (2006), 256.
|
[21] |
L. Ma and D. Chen, A Liouville type theorem for an integral system,, Commun. Pure Appl. Anal., 5 (2006), 855.
doi: 10.3934/cpaa.2006.5.855. |
[22] |
Q. A. Ngô and V. H. Nguyen, Sharp Reversed Hardy-Littlewood-Sobolev inequality on $\mathbfR^n$,, Israel J. Math., (). Google Scholar |
[23] |
J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations,, Math. Ann., 313 (1999), 207.
doi: 10.1007/s002080050258. |
[24] |
X. Xu, Uniqueness theorem for integral equations and its application,, J. Funct. Anal., 247 (2007), 95.
doi: 10.1016/j.jfa.2007.03.005. |
[25] |
Z. Zhang, Positive solutions of Lane-Emden systems with negative exponents: Existence, boundary behavior and uniqueness,, Nonlinear Anal., 74 (2011), 5544.
doi: 10.1016/j.na.2011.05.038. |
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