-
Previous Article
Boundary value problems for a semilinear elliptic equation with singular nonlinearity
- CPAA Home
- This Issue
-
Next Article
Optimal Szegö-Weinberger type inequalities
Existence and nonexistence of positive solutions to an integral system involving Wolff potential
1. | School of Mathematical Sciences, Jiangsu Normal University, Xuzhou 221116, China, China |
References:
[1] |
C. Cascante, J. Ortega and I. Verbitsky, Wolff's inequality for radially nonincreasing kernels and applications to trace inequalities, Potential Analysis., 16 (2002), 347-372.
doi: 10.1023/A:1014845728367. |
[2] |
L. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math., 42 (1989), 271-297.
doi: 10.1002/cpa.3160420304. |
[3] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math., 59 (2006), 330-343.
doi: 10.1002/cpa.20116. |
[4] |
W. Chen and C. Li, Regularity of solutions for a system of integral equations, Comm. Pure Appl. Anal., 4 (2005),1-8. |
[5] |
W. Chen and C. Li, Radial symmetry of solutions for some integral systems of Wolff type, Disc. Cont. Dyn. Sys., 30 (2011), 1083-1093.
doi: 10.3934/dcds.2011.30.1083. |
[6] |
W. Chen and C. Li, Super polyharmonic property of solutions for PDE systems and its applications, Comm. Pure Appl. Anal., 12 (2013), 2497-2514.
doi: 10.3934/cpaa.2013.12.2497. |
[7] |
L. I. Hedberg and T. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier (Grenoble), 33 (1983), 161-187. |
[8] |
X. Huang, D. Li and L. Wang, Existence and symmetry of positive solutions of an integral equation system, Math. Comput. Modelling, 52 (2010), 892-901.
doi: 10.1016/j.mcm.2010.05.020. |
[9] |
X. Huang, G. Hong and D. Li, Some symmetry results for integral equations involving Wolff potential on bounded domains, Nonlinear Anal., 75 (2012), 5601-5611.
doi: 10.1016/j.na.2012.05.007. |
[10] |
T. Kilpelaiinen and J. Maly, The Wiener test and potential estimates for quasilinear ellipitc equations, Acta Math., 172 (1994), 137-161.
doi: 10.1007/BF02392793. |
[11] |
T. Kilpelaiinen and J. Maly, Degenerate elliptic equations with measure data and nonlinear potentials, Ann. Sc. Norm. Super. Pisa Cl. Sci., 19 (1992), 591-613. |
[12] |
D. Labutin, Potential eatimates for a class of fully nonlinear elliptic equations, Duke Math. J., 111 (2002), 1-49.
doi: 10.1215/S0012-7094-02-11111-9. |
[13] |
Y. Lei, C. Li and C. Ma, Decay estimation for positve solutions of a $\gamma$-Laplace equation, Disc. Cont. Dyn. Syst., 30 (2011), 547-558.
doi: 10.3934/dcds.2011.30.547. |
[14] |
Y. Lei and C. Li, Sharp criteria of Liouville type for some nonlinear systems, arXiv:1301.6235. |
[15] |
Y. Lei, Decay rates for solutions of an integral system of Wolff type, Potential Analysis, 35 (2011), 387-402.
doi: 10.1007/s11118-010-9218-5. |
[16] |
C. Ma, W. Chen and C. Li, Regularity of solutions for an integral system of Wolff type, Advances in Mathematics, 226 (2011), 2676-2699.
doi: 10.1016/j.aim.2010.07.020. |
[17] |
N. Phuc and I. Verbitsky, Quasilinear and Hessian equations of Lane-Emden type, Ann. of Math., 168 (2008), 859-914.
doi: 10.4007/annals.2008.168.859. |
show all references
References:
[1] |
C. Cascante, J. Ortega and I. Verbitsky, Wolff's inequality for radially nonincreasing kernels and applications to trace inequalities, Potential Analysis., 16 (2002), 347-372.
doi: 10.1023/A:1014845728367. |
[2] |
L. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math., 42 (1989), 271-297.
doi: 10.1002/cpa.3160420304. |
[3] |
W. Chen, C. Li and B. Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math., 59 (2006), 330-343.
doi: 10.1002/cpa.20116. |
[4] |
W. Chen and C. Li, Regularity of solutions for a system of integral equations, Comm. Pure Appl. Anal., 4 (2005),1-8. |
[5] |
W. Chen and C. Li, Radial symmetry of solutions for some integral systems of Wolff type, Disc. Cont. Dyn. Sys., 30 (2011), 1083-1093.
doi: 10.3934/dcds.2011.30.1083. |
[6] |
W. Chen and C. Li, Super polyharmonic property of solutions for PDE systems and its applications, Comm. Pure Appl. Anal., 12 (2013), 2497-2514.
doi: 10.3934/cpaa.2013.12.2497. |
[7] |
L. I. Hedberg and T. Wolff, Thin sets in nonlinear potential theory, Ann. Inst. Fourier (Grenoble), 33 (1983), 161-187. |
[8] |
X. Huang, D. Li and L. Wang, Existence and symmetry of positive solutions of an integral equation system, Math. Comput. Modelling, 52 (2010), 892-901.
doi: 10.1016/j.mcm.2010.05.020. |
[9] |
X. Huang, G. Hong and D. Li, Some symmetry results for integral equations involving Wolff potential on bounded domains, Nonlinear Anal., 75 (2012), 5601-5611.
doi: 10.1016/j.na.2012.05.007. |
[10] |
T. Kilpelaiinen and J. Maly, The Wiener test and potential estimates for quasilinear ellipitc equations, Acta Math., 172 (1994), 137-161.
doi: 10.1007/BF02392793. |
[11] |
T. Kilpelaiinen and J. Maly, Degenerate elliptic equations with measure data and nonlinear potentials, Ann. Sc. Norm. Super. Pisa Cl. Sci., 19 (1992), 591-613. |
[12] |
D. Labutin, Potential eatimates for a class of fully nonlinear elliptic equations, Duke Math. J., 111 (2002), 1-49.
doi: 10.1215/S0012-7094-02-11111-9. |
[13] |
Y. Lei, C. Li and C. Ma, Decay estimation for positve solutions of a $\gamma$-Laplace equation, Disc. Cont. Dyn. Syst., 30 (2011), 547-558.
doi: 10.3934/dcds.2011.30.547. |
[14] |
Y. Lei and C. Li, Sharp criteria of Liouville type for some nonlinear systems, arXiv:1301.6235. |
[15] |
Y. Lei, Decay rates for solutions of an integral system of Wolff type, Potential Analysis, 35 (2011), 387-402.
doi: 10.1007/s11118-010-9218-5. |
[16] |
C. Ma, W. Chen and C. Li, Regularity of solutions for an integral system of Wolff type, Advances in Mathematics, 226 (2011), 2676-2699.
doi: 10.1016/j.aim.2010.07.020. |
[17] |
N. Phuc and I. Verbitsky, Quasilinear and Hessian equations of Lane-Emden type, Ann. of Math., 168 (2008), 859-914.
doi: 10.4007/annals.2008.168.859. |
[1] |
Wenxiong Chen, Congming Li. Radial symmetry of solutions for some integral systems of Wolff type. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1083-1093. doi: 10.3934/dcds.2011.30.1083 |
[2] |
Meixia Dou. A direct method of moving planes for fractional Laplacian equations in the unit ball. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1797-1807. doi: 10.3934/cpaa.2016015 |
[3] |
Baiyu Liu. Direct method of moving planes for logarithmic Laplacian system in bounded domains. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 5339-5349. doi: 10.3934/dcds.2018235 |
[4] |
Pengyan Wang, Pengcheng Niu. A direct method of moving planes for a fully nonlinear nonlocal system. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1707-1718. doi: 10.3934/cpaa.2017082 |
[5] |
Yuxia Guo, Shaolong Peng. A direct method of moving planes for fully nonlinear nonlocal operators and applications. Discrete and Continuous Dynamical Systems - S, 2021, 14 (6) : 1871-1897. doi: 10.3934/dcdss.2020462 |
[6] |
Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810 |
[7] |
Antonio Greco, Vincenzino Mascia. Non-local sublinear problems: Existence, comparison, and radial symmetry. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 503-519. doi: 10.3934/dcds.2019021 |
[8] |
Xiaotao Huang, Lihe Wang. Radial symmetry results for Bessel potential integral equations in exterior domains and in annular domains. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1121-1134. doi: 10.3934/cpaa.2017054 |
[9] |
Trad Alotaibi, D. D. Hai, R. Shivaji. Existence and nonexistence of positive radial solutions for a class of $p$-Laplacian superlinear problems with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4655-4666. doi: 10.3934/cpaa.2020131 |
[10] |
Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3821-3836. doi: 10.3934/dcdss.2020436 |
[11] |
Yutian Lei. Wolff type potential estimates and application to nonlinear equations with negative exponents. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2067-2078. doi: 10.3934/dcds.2015.35.2067 |
[12] |
Huan Chen, Zhongxue Lü. The properties of positive solutions to an integral system involving Wolff potential. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1879-1904. doi: 10.3934/dcds.2014.34.1879 |
[13] |
Miaomiao Cai, Li Ma. Moving planes for nonlinear fractional Laplacian equation with negative powers. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4603-4615. doi: 10.3934/dcds.2018201 |
[14] |
Pei Ma, Yan Li, Jihui Zhang. Symmetry and nonexistence of positive solutions for fractional systems. Communications on Pure and Applied Analysis, 2018, 17 (3) : 1053-1070. doi: 10.3934/cpaa.2018051 |
[15] |
Anh Tuan Duong, Phuong Le, Nhu Thang Nguyen. Symmetry and nonexistence results for a fractional Choquard equation with weights. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 489-505. doi: 10.3934/dcds.2020265 |
[16] |
Xiaoxue Ji, Pengcheng Niu, Pengyan Wang. Non-existence results for cooperative semi-linear fractional system via direct method of moving spheres. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1111-1128. doi: 10.3934/cpaa.2020051 |
[17] |
Orlando Lopes. Uniqueness and radial symmetry of minimizers for a nonlocal variational problem. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2265-2282. doi: 10.3934/cpaa.2019102 |
[18] |
Zhenjie Li, Chunqin Zhou. Radial symmetry of nonnegative solutions for nonlinear integral systems. Communications on Pure and Applied Analysis, 2022, 21 (3) : 837-844. doi: 10.3934/cpaa.2021201 |
[19] |
Leyun Wu, Pengcheng Niu. Symmetry and nonexistence of positive solutions to fractional p-Laplacian equations. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1573-1583. doi: 10.3934/dcds.2019069 |
[20] |
Ran Zhuo, Yan Li. Nonexistence and symmetry of solutions for Schrödinger systems involving fractional Laplacian. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1595-1611. doi: 10.3934/dcds.2019071 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]