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Asymptotic behavior of the ground state Solutions for Hénon equation with Robin boundary condition
1. | College of Mathematics and Computer Science, Key Laboratory of High Performance Computing, and Stochastic Information Processing(Ministry of Education of China), Hunan Normal University, Changsha, Hunan 410081, China |
References:
[1] |
Adimurthi and G. Mancini, The Neumann problem for elliptic equations with critical nonlinearity, A tribute in honour of G. Prodi, Nonlinear Anal., Scuola Norm. Sup. Pisa, (1991), 9-25. |
[2] |
Adimurthi and G. Mancini, Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math., 456 (1994), 1-18.
doi: 10.1515/crll.1994.456.1. |
[3] |
Adimurthi and S. L. Yadava, Positive solution for Neumann problem with critical nonlinearity on boundary, Comm. Partial Differential Equations, 16 (1991), 1733-1760.
doi: 10.1080/03605309108820821. |
[4] |
H. Brezis and E. Lieb, Sobolev inequalities with remainder terms, J. Funct. Anal., 62 (1985), 73-86.
doi: 10.1016/0022-1236(85)90020-5. |
[5] |
J. Byeon and Z-Q. Wang, On the Hénon equation: Asymptotic profile of ground state I, Ann. I. H. Poincare., 23 (2006), 803-828.
doi: 10.1016/j.anihpc.2006.04.001. |
[6] |
J. Byeon and Z-Q. Wang, On the Hénon equation: Asymptotic profile of ground state II, J. Differential Equation, 216 (2005), 78-108.
doi: 10.1016/j.jde.2005.02.018. |
[7] |
D. Cao and S. Peng, The asymptotic behavior of the ground state solutions for Hénon equation, J. Math. Anal. Appl., 278 (2003), 1-17.
doi: 10.1016/S0022-247X(02)00292-5. |
[8] |
Daomin Cao, E. S. Noussair and Shusen Yan, On a semilinear Robin prolem involving critical Sobolev exponent, Advanced Nonlinear Studies, 1 (2001), 43-77. |
[9] |
Yuxia Fu and Qiuyi Dai, Positive solutions of the Robin problem for semilinear elliptic equations on annuli, Rend. Lincei Mat. Appl., 19 (2008), 175-188.
doi: 10.4171/RLM/516. |
[10] |
B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations, 8 (1981), 883-901.
doi: 10.1080/03605308108820196. |
[11] |
Yonggen Gu and T. Liu, A priori estimate and existence of positive solutions of semilinear elliptic equations with the third boundary value problem, J. Systems Sci. Complexity, 14 (2001), 389-318. |
[12] |
M. Hénon, Numerical experiments on the stability of spherical stellar systems, Astronom. Astrophys., 24 (1973), 229-238.
doi: 10.1007/978-94-010-9877-9_37. |
[13] |
Haiyang He, The Robin problem for the Hénon equation,, Accepted by Bulletin of the Australian Mathematic Society., ().
|
[14] |
P. L. Lions, The concentration compactness principle in the calculus of variations, the limit case, Rev. Mat. Iberoamericana., (1985), 145-201.
doi: 10.4171/RMI/6. |
[15] |
W. M. Ni and I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math., 44 (1991), 819-851.
doi: 10.1002/cpa.3160440705. |
[16] |
D. Smets, J. B. Su and M. Willem, Non-radial ground states for the Henon equation, Comm. Contemp. Math., 4 (2002), 467-480.
doi: 10.1142/S0219199702000725. |
[17] |
D. Smets and M. Willem, Partial symmetry and asymptotic behavior for some elliptic variational problem, Calc. Var. Partial Differential Equations, 18 (2003), 57-75.
doi: 10.1007/s00526-002-0180-y. |
[18] |
X. J. Wang, Neumann problem for semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equation, 93 (1991), 283-310.
doi: 10.1016/0022-0396(91)90014-Z. |
show all references
References:
[1] |
Adimurthi and G. Mancini, The Neumann problem for elliptic equations with critical nonlinearity, A tribute in honour of G. Prodi, Nonlinear Anal., Scuola Norm. Sup. Pisa, (1991), 9-25. |
[2] |
Adimurthi and G. Mancini, Geometry and topology of the boundary in the critical Neumann problem, J. Reine Angew. Math., 456 (1994), 1-18.
doi: 10.1515/crll.1994.456.1. |
[3] |
Adimurthi and S. L. Yadava, Positive solution for Neumann problem with critical nonlinearity on boundary, Comm. Partial Differential Equations, 16 (1991), 1733-1760.
doi: 10.1080/03605309108820821. |
[4] |
H. Brezis and E. Lieb, Sobolev inequalities with remainder terms, J. Funct. Anal., 62 (1985), 73-86.
doi: 10.1016/0022-1236(85)90020-5. |
[5] |
J. Byeon and Z-Q. Wang, On the Hénon equation: Asymptotic profile of ground state I, Ann. I. H. Poincare., 23 (2006), 803-828.
doi: 10.1016/j.anihpc.2006.04.001. |
[6] |
J. Byeon and Z-Q. Wang, On the Hénon equation: Asymptotic profile of ground state II, J. Differential Equation, 216 (2005), 78-108.
doi: 10.1016/j.jde.2005.02.018. |
[7] |
D. Cao and S. Peng, The asymptotic behavior of the ground state solutions for Hénon equation, J. Math. Anal. Appl., 278 (2003), 1-17.
doi: 10.1016/S0022-247X(02)00292-5. |
[8] |
Daomin Cao, E. S. Noussair and Shusen Yan, On a semilinear Robin prolem involving critical Sobolev exponent, Advanced Nonlinear Studies, 1 (2001), 43-77. |
[9] |
Yuxia Fu and Qiuyi Dai, Positive solutions of the Robin problem for semilinear elliptic equations on annuli, Rend. Lincei Mat. Appl., 19 (2008), 175-188.
doi: 10.4171/RLM/516. |
[10] |
B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations, 8 (1981), 883-901.
doi: 10.1080/03605308108820196. |
[11] |
Yonggen Gu and T. Liu, A priori estimate and existence of positive solutions of semilinear elliptic equations with the third boundary value problem, J. Systems Sci. Complexity, 14 (2001), 389-318. |
[12] |
M. Hénon, Numerical experiments on the stability of spherical stellar systems, Astronom. Astrophys., 24 (1973), 229-238.
doi: 10.1007/978-94-010-9877-9_37. |
[13] |
Haiyang He, The Robin problem for the Hénon equation,, Accepted by Bulletin of the Australian Mathematic Society., ().
|
[14] |
P. L. Lions, The concentration compactness principle in the calculus of variations, the limit case, Rev. Mat. Iberoamericana., (1985), 145-201.
doi: 10.4171/RMI/6. |
[15] |
W. M. Ni and I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math., 44 (1991), 819-851.
doi: 10.1002/cpa.3160440705. |
[16] |
D. Smets, J. B. Su and M. Willem, Non-radial ground states for the Henon equation, Comm. Contemp. Math., 4 (2002), 467-480.
doi: 10.1142/S0219199702000725. |
[17] |
D. Smets and M. Willem, Partial symmetry and asymptotic behavior for some elliptic variational problem, Calc. Var. Partial Differential Equations, 18 (2003), 57-75.
doi: 10.1007/s00526-002-0180-y. |
[18] |
X. J. Wang, Neumann problem for semilinear elliptic equations involving critical Sobolev exponents, J. Differential Equation, 93 (1991), 283-310.
doi: 10.1016/0022-0396(91)90014-Z. |
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