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Nonexistence of positive solution for an integral equation on a Half-Space $R_+^n$
1. | Jiangsu Key Laboratory for NSLSCS, School of Mathematics Sciences, Nanjing Normal University, Nanjing 210046, Jiangsu |
References:
[1] |
H. Berestycki and L. Nirenberg, On the method of moving planes and sliding method, Bol. Soc. Brazil. Mat. (N. S.), 22 (1991), 1-37.
doi: 10.1007/BF01244896. |
[2] |
G. Bianchi, Non-existence of positive solutions to semilinear elliptic equations in $R^N$ and $R_+ ^N$ through the method of moving plane, Comn. PDE., 22 (1997), 9-10, 1671-1690.
doi: 10.1080/03605309708821315. |
[3] |
L. Cao, A Liouville-Type Theorem for an integral equation on a Half-Space $R_+ ^n$, , Submitted., ().
|
[4] |
W. Chen and C. Li, Radial symmetry of solutions for some integral systems of wolff type, Dis. Cont. Dyn. Sys., 30 (2011), 1083-1093.
doi: 10.3934/dcds.2011.30.1083. |
[5] |
W. Chen and J. Zhu, Radial symmetry and regularity of solutions for poly-harmonic Drichlet Problems, J. Math. Anal. Appl., 377 (2011), 744-753.
doi: 10.1016/j.jmaa.2010.11.035. |
[6] |
W. Chen and C. Li, Methods on Nonlinear Elliptic Equations, Diff. Equa. Dyn. Syst., 2010. |
[7] |
W. Chen and C. Li, Classification of positive solutions for nonlinear differential and integral systems with critical exponents, Acta Mathematics Scientia, 29 (2009), 949-960.
doi: 10.1016/S0252-9602(09)60079-5. |
[8] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math. 59 (2006), 330-343. |
[9] |
W. Chen and C. Li, Regularity of solutions for a system of integral equation, Commun. Pure Appl. Anal., 4 (2005), 1-8. |
[10] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations, Comm. Partial Differential Equations, 30 (2005), 59-65.
doi: 10.1081/PDE-200044445. |
[11] |
W. Chen and C. Li, Classification of solutions to some nonlinear equations, Duke Math. J., 63 (1991), 615–-622.
doi: 10.1215/S0012-7094-91-06325-8. |
[12] |
D. Li and R. Zhuo, An integral eequation on Half space, Proc. Amer. Math. Soc., 138 (2010), 2779-2791. |
[13] |
C. S. Lin, A classification of solutions of a conformally invariant fourth order equation in $R^n$, Comment. Math. Helv., 73 (1998), 206-231.
doi: 10.5169/seals-55100. |
[14] |
Y. Ge, Positive solutions in semilinear critical problems for polyharmonic operators, J. Math. Pures Appl., 84 (2005), 199–-245.
doi: 10.1016/j.matpur.2004.10.002. |
[15] |
Y. Guo and J. Liu, Liouville-type theorems for polyharmonic equations in $R^N$ and in $R_+ ^N$, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 339-359.
doi: 10.1017/S0308210506000394. |
[16] |
B. Gidas and J. Spruk, A prior bounds for positive solutions of nonlinear elliptic equations, Commun. PDEs, 6 (1981), 883-901. |
[17] |
C. Ma, W. Chen and C. Li, Regularity of solutions for an integral system of Wolff type, Adv. Math., 226 (2011), 2676-2699.
doi: 10.1016/j.aim.2010.07.020. |
[18] |
L. Ma and D. Chen, A Liouville type theorem for an integral system, Commun. Pure Appl. Anal., 5 (2006), 855-859. |
[19] |
W. Reichel and T. Weth, A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems, Math. Z., 261 (2009), 805-827.
doi: 10.1007/s00209-008-0352-3. |
[20] |
J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations, Math. Ann., 313 (1999), 207-228. |
show all references
References:
[1] |
H. Berestycki and L. Nirenberg, On the method of moving planes and sliding method, Bol. Soc. Brazil. Mat. (N. S.), 22 (1991), 1-37.
doi: 10.1007/BF01244896. |
[2] |
G. Bianchi, Non-existence of positive solutions to semilinear elliptic equations in $R^N$ and $R_+ ^N$ through the method of moving plane, Comn. PDE., 22 (1997), 9-10, 1671-1690.
doi: 10.1080/03605309708821315. |
[3] |
L. Cao, A Liouville-Type Theorem for an integral equation on a Half-Space $R_+ ^n$, , Submitted., ().
|
[4] |
W. Chen and C. Li, Radial symmetry of solutions for some integral systems of wolff type, Dis. Cont. Dyn. Sys., 30 (2011), 1083-1093.
doi: 10.3934/dcds.2011.30.1083. |
[5] |
W. Chen and J. Zhu, Radial symmetry and regularity of solutions for poly-harmonic Drichlet Problems, J. Math. Anal. Appl., 377 (2011), 744-753.
doi: 10.1016/j.jmaa.2010.11.035. |
[6] |
W. Chen and C. Li, Methods on Nonlinear Elliptic Equations, Diff. Equa. Dyn. Syst., 2010. |
[7] |
W. Chen and C. Li, Classification of positive solutions for nonlinear differential and integral systems with critical exponents, Acta Mathematics Scientia, 29 (2009), 949-960.
doi: 10.1016/S0252-9602(09)60079-5. |
[8] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math. 59 (2006), 330-343. |
[9] |
W. Chen and C. Li, Regularity of solutions for a system of integral equation, Commun. Pure Appl. Anal., 4 (2005), 1-8. |
[10] |
W. Chen, C. Li and B. Ou, Classification of solutions for a system of integral equations, Comm. Partial Differential Equations, 30 (2005), 59-65.
doi: 10.1081/PDE-200044445. |
[11] |
W. Chen and C. Li, Classification of solutions to some nonlinear equations, Duke Math. J., 63 (1991), 615–-622.
doi: 10.1215/S0012-7094-91-06325-8. |
[12] |
D. Li and R. Zhuo, An integral eequation on Half space, Proc. Amer. Math. Soc., 138 (2010), 2779-2791. |
[13] |
C. S. Lin, A classification of solutions of a conformally invariant fourth order equation in $R^n$, Comment. Math. Helv., 73 (1998), 206-231.
doi: 10.5169/seals-55100. |
[14] |
Y. Ge, Positive solutions in semilinear critical problems for polyharmonic operators, J. Math. Pures Appl., 84 (2005), 199–-245.
doi: 10.1016/j.matpur.2004.10.002. |
[15] |
Y. Guo and J. Liu, Liouville-type theorems for polyharmonic equations in $R^N$ and in $R_+ ^N$, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 339-359.
doi: 10.1017/S0308210506000394. |
[16] |
B. Gidas and J. Spruk, A prior bounds for positive solutions of nonlinear elliptic equations, Commun. PDEs, 6 (1981), 883-901. |
[17] |
C. Ma, W. Chen and C. Li, Regularity of solutions for an integral system of Wolff type, Adv. Math., 226 (2011), 2676-2699.
doi: 10.1016/j.aim.2010.07.020. |
[18] |
L. Ma and D. Chen, A Liouville type theorem for an integral system, Commun. Pure Appl. Anal., 5 (2006), 855-859. |
[19] |
W. Reichel and T. Weth, A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems, Math. Z., 261 (2009), 805-827.
doi: 10.1007/s00209-008-0352-3. |
[20] |
J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations, Math. Ann., 313 (1999), 207-228. |
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