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Four positive solutions of a quasilinear elliptic equation in $ R^N$
Nonexistence of positive solutions for a system of integral equations on $R^n_+$ and applications
1. | Department of Applied Mathematics, Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education, Northwestern Polytechnical University, Xi'an, Shaanxi 710129, China, China |
References:
[1] |
W. Reichel and T. Weth, A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirchlet problems,, Math.Z., 261 (2009), 805.
doi: 10.1007/s00209-008-0352-3. |
[2] |
Y. Fang and W. Chen, A Liouville type theorem for poly-harmonic Dirichlet problems in a half space,, Adv. Math., 229 (2012), 2835.
doi: 10.1016/j.aim.2012.01.018. |
[3] |
Y. Fang and J. Zhang, Nonexistence of positive solition for an integral equation on $R^n_+$,, Commun. Pure Appl. Anal., 12 (2013), 663.
doi: 10.3934/cpaa.2013.12.663. |
[4] |
C. S. Lin, A classification of solutions of a conformally invariant fourth order equation in $R^n$,, Comment. Math. Helv, 73 (1998), 206.
doi: 10.1007/s000140050052. |
[5] |
J. Wei and X. Xu, Classification of solution of higer order conformally invariant equations,, Math. Ann., 313 (1999), 207.
doi: 10.1007/s002080050258. |
[6] |
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.20130. |
[7] |
W. Chen, C. Li and B. Ou, Qualitative problems of solutions for a system of integral equation,, Discrete Contin. Dyn. Syst., 12 (2005), 347. Google Scholar |
[8] |
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. |
[9] |
W. Chen and C. Li, Super polyharmonic property of solutions for PDE systems and its applications,, appear to in Commun. Pure Appl. Anal., (2012). Google Scholar |
[10] |
W. Chen and C. Li, Regularity of solutions for a system of integral equations,, Commun. Pure Appl. Anal., 4 (2005), 1.
doi: 10.3934/cpaa.2005.4.1. |
[11] |
W. Chen and C. Li, An integral system and the Lane-Emden conjecture,, Discrete Contin. Dyn. Syst., 4 (2009), 1167.
doi: 10.3934/dcds.2009.24.1167. |
[12] |
C. Jin and C. Li, Symmetry of solutions to some system of integral equations,, Proc. Amer. Math. Soc., 134 (2006), 1661.
doi: 10.1090/S0002-9939-05-08411-X. |
[13] |
W. Chen and C. Li, "Methods on Nonlinear Elliptic Equations,", AIMS Book Series on Differ. Equ. Dyn. Syst., 4 (2010).
doi: 10.3934/dcds.2009.24.1167. |
[14] |
C. Jin and C. Li, Quantitative analysis of some system of integral equations,, Calc. Var. Partial Differential Equations, 26 (2006), 447.
doi: 10.1007/s00526-006-0013-5. |
[15] |
C. Li and L. Ma, Uniqueness of positive bound states to Shrodinger systems with critical exponents,, SIAM J. Math. Anal., 40 (2008), 1049.
doi: 10.1137/080712301. |
[16] |
W. Chen, C. Li and J. Lim, Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations,, Discrete Contin. Dyn. Syst., 12 (2005), 347.
|
[17] |
C. Liu and S. Qiao, Symmetry and monotonicity for a system of integal equations,, Commun. Pure Appl. Anal., 6 (2009), 1925.
doi: 10.3934/cpaa.2009.8.1925. |
[18] |
L. Ma and D. Z. Chen, A Liouville type theorem for an integral system,, Commun. Pure Appl. Anal., 5 (2006), 855.
doi: 10.3934/cpaa.2006.5.855. |
[19] |
L. Ma and D. Z. Chen, Radial symmetry and monotonicity for an integral equation,, J. Math. Anal. Appl., 342 (2008), 943.
doi: 10.1016/j.jmaa.2007.12.064. |
[20] |
B. Ou, A Remark on a singular integral equation,, Houston J. Math., 25 (1999), 181.
|
[21] |
J. Liu, Y. Guo and Y. Zhang, Liouville type theorems for polyharmonic system in $R^n$,, J. Differential Equations, 225 (2006), 685.
doi: 10.1016/j.jde.2005.10.016. |
show all references
References:
[1] |
W. Reichel and T. Weth, A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirchlet problems,, Math.Z., 261 (2009), 805.
doi: 10.1007/s00209-008-0352-3. |
[2] |
Y. Fang and W. Chen, A Liouville type theorem for poly-harmonic Dirichlet problems in a half space,, Adv. Math., 229 (2012), 2835.
doi: 10.1016/j.aim.2012.01.018. |
[3] |
Y. Fang and J. Zhang, Nonexistence of positive solition for an integral equation on $R^n_+$,, Commun. Pure Appl. Anal., 12 (2013), 663.
doi: 10.3934/cpaa.2013.12.663. |
[4] |
C. S. Lin, A classification of solutions of a conformally invariant fourth order equation in $R^n$,, Comment. Math. Helv, 73 (1998), 206.
doi: 10.1007/s000140050052. |
[5] |
J. Wei and X. Xu, Classification of solution of higer order conformally invariant equations,, Math. Ann., 313 (1999), 207.
doi: 10.1007/s002080050258. |
[6] |
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.20130. |
[7] |
W. Chen, C. Li and B. Ou, Qualitative problems of solutions for a system of integral equation,, Discrete Contin. Dyn. Syst., 12 (2005), 347. Google Scholar |
[8] |
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. |
[9] |
W. Chen and C. Li, Super polyharmonic property of solutions for PDE systems and its applications,, appear to in Commun. Pure Appl. Anal., (2012). Google Scholar |
[10] |
W. Chen and C. Li, Regularity of solutions for a system of integral equations,, Commun. Pure Appl. Anal., 4 (2005), 1.
doi: 10.3934/cpaa.2005.4.1. |
[11] |
W. Chen and C. Li, An integral system and the Lane-Emden conjecture,, Discrete Contin. Dyn. Syst., 4 (2009), 1167.
doi: 10.3934/dcds.2009.24.1167. |
[12] |
C. Jin and C. Li, Symmetry of solutions to some system of integral equations,, Proc. Amer. Math. Soc., 134 (2006), 1661.
doi: 10.1090/S0002-9939-05-08411-X. |
[13] |
W. Chen and C. Li, "Methods on Nonlinear Elliptic Equations,", AIMS Book Series on Differ. Equ. Dyn. Syst., 4 (2010).
doi: 10.3934/dcds.2009.24.1167. |
[14] |
C. Jin and C. Li, Quantitative analysis of some system of integral equations,, Calc. Var. Partial Differential Equations, 26 (2006), 447.
doi: 10.1007/s00526-006-0013-5. |
[15] |
C. Li and L. Ma, Uniqueness of positive bound states to Shrodinger systems with critical exponents,, SIAM J. Math. Anal., 40 (2008), 1049.
doi: 10.1137/080712301. |
[16] |
W. Chen, C. Li and J. Lim, Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations,, Discrete Contin. Dyn. Syst., 12 (2005), 347.
|
[17] |
C. Liu and S. Qiao, Symmetry and monotonicity for a system of integal equations,, Commun. Pure Appl. Anal., 6 (2009), 1925.
doi: 10.3934/cpaa.2009.8.1925. |
[18] |
L. Ma and D. Z. Chen, A Liouville type theorem for an integral system,, Commun. Pure Appl. Anal., 5 (2006), 855.
doi: 10.3934/cpaa.2006.5.855. |
[19] |
L. Ma and D. Z. Chen, Radial symmetry and monotonicity for an integral equation,, J. Math. Anal. Appl., 342 (2008), 943.
doi: 10.1016/j.jmaa.2007.12.064. |
[20] |
B. Ou, A Remark on a singular integral equation,, Houston J. Math., 25 (1999), 181.
|
[21] |
J. Liu, Y. Guo and Y. Zhang, Liouville type theorems for polyharmonic system in $R^n$,, J. Differential Equations, 225 (2006), 685.
doi: 10.1016/j.jde.2005.10.016. |
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