-
Previous Article
Positive solutions to a Dirichlet problem with $p$-Laplacian and concave-convex nonlinearity depending on a parameter
- CPAA Home
- This Issue
-
Next Article
Multiplicity results for a class of elliptic problems with nonlinear boundary condition
Some results on two-dimensional Hénon equation with large exponent in nonlinearity
1. | Department of Mathematics, East China Normal University, Shanghai 200241, China |
References:
[1] |
Adimurthi and M. Grossi, Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity, Proc. Amer. Math. Soc., 132 (2004), 1013-1019 (electronic).
doi: 10.1090/S0002-9939-03-07301-5. |
[2] |
V. Barutello, S. Secchi and E. Serra, A note on the radial solutions for the supercritical Hénon equation, J. Math. Anal. Appl., 341 (2008), 720-728.
doi: 10.1016/j.jmaa.2007.10.052. |
[3] |
J. Byeon and Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states, I. Ann. Inst. H. Poincaré Anal. Non Linéaire, 23 (2006), 803-828.
doi: 10.1016/j.anihpc.2006.04.001. |
[4] |
J. Byeon and Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states. II, J. Differential Equations, 216 (2005), 78-108.
doi: 10.1016/j.jde.2005.02.018. |
[5] |
W. X. Chen and C. M. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991), 615-623.
doi: 10.1215/S0012-7094-91-06325-8. |
[6] |
G. Chen, W.-M. Ni and J.X. Zhou, Algorithms and visualization for solutions of nonlinear elliptic equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10 (2000), 1565-1612.
doi: 10.1142/S0218127400001006. |
[7] |
D. M. Cao and S. J. Peng, The asymptotic behaviour 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] |
D. M. Cao, S. J. Peng and S. S. Yan, Asymptotic behaviour of ground state solutions for the Hénon equation, IMA J. Appl. Math., 74 (2009), 468-480.
doi: 10.1093/imamat/hxn035. |
[9] |
M. Calanchi, S. Secchi and E. Terraneo, Multiple solutions for Hénon-like equation on the annulus, J. Differential Equations, 245 (2008), 1507-1525.
doi: 10.1016/j.jde.2008.06.018. |
[10] |
P. Esposito, A. Pistoia and J. C. Wei, Concentrating solutions for the Hénon equation in $\mathbb R^2$, J. Anal. Math., 100 (2006), 249-280.
doi: 10.1007/BF02916763. |
[11] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
doi: 10.1007/BF01221125. |
[12] |
M. Gazzini and E. Serra, The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 281-302.
doi: 10.1016/j.anihpc.2006.09.003. |
[13] |
M. Hénon, Numerical experiments on the stability of spherical stellar systems, Astronom. Astrophys., 24 (1973), 229-238. |
[14] |
S. J. Li and S. J. Peng, Asymptotic behavior on the Hénon equation with supercritical exponent, Sci. China Ser. A, 52 (2009), 2185-2194.
doi: 10.1007/s11425-009-0094-7. |
[15] |
W.-M. Ni, A nonlinear Dirichlet problem on the unit ball and its applications, Indiana Univ. Math. J., 31 (1982), 801-807.
doi: 10.1512/iumj.1982.31.31056. |
[16] |
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. |
[17] |
S. J. Peng, Multiple boundary concentrating solutions to Dirichlet problem of Hénon equation, Acta Math. Appl. Sin. Engl. Ser., 22 (2006), 137-162.
doi: 10.1007/s10255-005-0293-0. |
[18] |
J. Prajapat and G. Tarantello, On a class of elliptic problem in $\mathbb R^2$: symmetry and uniqueness results, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 967-985.
doi: 10.1017/S0308210500001219. |
[19] |
A. Pistoia and E. Serra, Multi-peak solutions for the Hénon equation with slightly subcritical growth, Math. Z., 256 (2007), 75-97.
doi: 10.1007/s00209-006-0060-9. |
[20] |
X. F. Ren and J. C. Wei, On a two-dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc., 343 (1994), 749-763.
doi: 10.1090/S0002-9947-1994-1232190-7. |
[21] |
X. F. Ren and J. C. Wei, Single-point condensation and least-energy solutions, Proc. Amer. Math. Soc., 124 (1996), 111-120.
doi: 10.1090/S0002-9939-96-03156-5. |
[22] |
E. Serra, Non radial positive solutions for the Hénon equation with critical growth, Calc. Var. Partial Differential Equations, 23 (2005), 301-326.
doi: 10.1007/s00526-004-0302-9. |
[23] |
D. Smets, J. B. Su and M. Willem, Non-radial ground states for the Hénon equation, Commun. Contemp. Math., 4 (2002), 467-480.
doi: 10.1142/S0219199702000725. |
[24] |
D. Smets and M. Willem, Partial symmetry and asymptotic behavior for some elliptic variational problems, Calc. Var. Partial Differential Equations, 18 (2003), 57-75.
doi: 10.1007/s00526-002-0180-y. |
show all references
References:
[1] |
Adimurthi and M. Grossi, Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity, Proc. Amer. Math. Soc., 132 (2004), 1013-1019 (electronic).
doi: 10.1090/S0002-9939-03-07301-5. |
[2] |
V. Barutello, S. Secchi and E. Serra, A note on the radial solutions for the supercritical Hénon equation, J. Math. Anal. Appl., 341 (2008), 720-728.
doi: 10.1016/j.jmaa.2007.10.052. |
[3] |
J. Byeon and Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states, I. Ann. Inst. H. Poincaré Anal. Non Linéaire, 23 (2006), 803-828.
doi: 10.1016/j.anihpc.2006.04.001. |
[4] |
J. Byeon and Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states. II, J. Differential Equations, 216 (2005), 78-108.
doi: 10.1016/j.jde.2005.02.018. |
[5] |
W. X. Chen and C. M. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991), 615-623.
doi: 10.1215/S0012-7094-91-06325-8. |
[6] |
G. Chen, W.-M. Ni and J.X. Zhou, Algorithms and visualization for solutions of nonlinear elliptic equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10 (2000), 1565-1612.
doi: 10.1142/S0218127400001006. |
[7] |
D. M. Cao and S. J. Peng, The asymptotic behaviour 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] |
D. M. Cao, S. J. Peng and S. S. Yan, Asymptotic behaviour of ground state solutions for the Hénon equation, IMA J. Appl. Math., 74 (2009), 468-480.
doi: 10.1093/imamat/hxn035. |
[9] |
M. Calanchi, S. Secchi and E. Terraneo, Multiple solutions for Hénon-like equation on the annulus, J. Differential Equations, 245 (2008), 1507-1525.
doi: 10.1016/j.jde.2008.06.018. |
[10] |
P. Esposito, A. Pistoia and J. C. Wei, Concentrating solutions for the Hénon equation in $\mathbb R^2$, J. Anal. Math., 100 (2006), 249-280.
doi: 10.1007/BF02916763. |
[11] |
B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
doi: 10.1007/BF01221125. |
[12] |
M. Gazzini and E. Serra, The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues, Ann. Inst. H. Poincaré Anal. Non Linéaire, 25 (2008), 281-302.
doi: 10.1016/j.anihpc.2006.09.003. |
[13] |
M. Hénon, Numerical experiments on the stability of spherical stellar systems, Astronom. Astrophys., 24 (1973), 229-238. |
[14] |
S. J. Li and S. J. Peng, Asymptotic behavior on the Hénon equation with supercritical exponent, Sci. China Ser. A, 52 (2009), 2185-2194.
doi: 10.1007/s11425-009-0094-7. |
[15] |
W.-M. Ni, A nonlinear Dirichlet problem on the unit ball and its applications, Indiana Univ. Math. J., 31 (1982), 801-807.
doi: 10.1512/iumj.1982.31.31056. |
[16] |
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. |
[17] |
S. J. Peng, Multiple boundary concentrating solutions to Dirichlet problem of Hénon equation, Acta Math. Appl. Sin. Engl. Ser., 22 (2006), 137-162.
doi: 10.1007/s10255-005-0293-0. |
[18] |
J. Prajapat and G. Tarantello, On a class of elliptic problem in $\mathbb R^2$: symmetry and uniqueness results, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 967-985.
doi: 10.1017/S0308210500001219. |
[19] |
A. Pistoia and E. Serra, Multi-peak solutions for the Hénon equation with slightly subcritical growth, Math. Z., 256 (2007), 75-97.
doi: 10.1007/s00209-006-0060-9. |
[20] |
X. F. Ren and J. C. Wei, On a two-dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc., 343 (1994), 749-763.
doi: 10.1090/S0002-9947-1994-1232190-7. |
[21] |
X. F. Ren and J. C. Wei, Single-point condensation and least-energy solutions, Proc. Amer. Math. Soc., 124 (1996), 111-120.
doi: 10.1090/S0002-9939-96-03156-5. |
[22] |
E. Serra, Non radial positive solutions for the Hénon equation with critical growth, Calc. Var. Partial Differential Equations, 23 (2005), 301-326.
doi: 10.1007/s00526-004-0302-9. |
[23] |
D. Smets, J. B. Su and M. Willem, Non-radial ground states for the Hénon equation, Commun. Contemp. Math., 4 (2002), 467-480.
doi: 10.1142/S0219199702000725. |
[24] |
D. Smets and M. Willem, Partial symmetry and asymptotic behavior for some elliptic variational problems, Calc. Var. Partial Differential Equations, 18 (2003), 57-75.
doi: 10.1007/s00526-002-0180-y. |
[1] |
Jaeyoung Byeon, Sungwon Cho, Junsang Park. On the location of a peak point of a least energy solution for Hénon equation. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1055-1081. doi: 10.3934/dcds.2011.30.1055 |
[2] |
Futoshi Takahashi. On the number of maximum points of least energy solution to a two-dimensional Hénon equation with large exponent. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1237-1241. doi: 10.3934/cpaa.2013.12.1237 |
[3] |
Guangyu Xu. Emergence of lager densities in chemotaxis system with indirect signal production and non-radial symmetry case. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022096 |
[4] |
Joel Kübler, Tobias Weth. Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3629-3656. doi: 10.3934/dcds.2020032 |
[5] |
Daniela Gurban, Petru Jebelean, Cǎlin Şerban. Non-potential and non-radial Dirichlet systems with mean curvature operator in Minkowski space. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 133-151. doi: 10.3934/dcds.2020006 |
[6] |
Shun Kodama. A concentration phenomenon of the least energy solution to non-autonomous elliptic problems with a totally degenerate potential. Communications on Pure and Applied Analysis, 2017, 16 (2) : 671-698. doi: 10.3934/cpaa.2017033 |
[7] |
Yuxia Guo, Jianjun Nie. Infinitely many non-radial solutions for the prescribed curvature problem of fractional operator. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6873-6898. doi: 10.3934/dcds.2016099 |
[8] |
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 |
[9] |
Eudes. M. Barboza, Olimpio H. Miyagaki, Fábio R. Pereira, Cláudia R. Santana. Radial solutions for a class of Hénon type systems with partial interference with the spectrum. Communications on Pure and Applied Analysis, 2020, 19 (6) : 3159-3187. doi: 10.3934/cpaa.2020137 |
[10] |
Kods Hassine. Existence and uniqueness of radial solutions for Hardy-Hénon equations involving k-Hessian operators. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022084 |
[11] |
Henri Berestycki, Juncheng Wei. On least energy solutions to a semilinear elliptic equation in a strip. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1083-1099. doi: 10.3934/dcds.2010.28.1083 |
[12] |
Jaeyoung Byeon, Sangdon Jin. The Hénon equation with a critical exponent under the Neumann boundary condition. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4353-4390. doi: 10.3934/dcds.2018190 |
[13] |
Jingbo Dou, Huaiyu Zhou. Liouville theorems for fractional Hénon equation and system on $\mathbb{R}^n$. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1915-1927. doi: 10.3934/cpaa.2015.14.1915 |
[14] |
Shoichi Hasegawa, Norihisa Ikoma, Tatsuki Kawakami. On weak solutions to a fractional Hardy–Hénon equation: Part I: Nonexistence. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1559-1600. doi: 10.3934/cpaa.2021033 |
[15] |
Craig Cowan, Abdolrahman Razani. Singular solutions of a Hénon equation involving a nonlinear gradient term. Communications on Pure and Applied Analysis, 2022, 21 (1) : 141-158. doi: 10.3934/cpaa.2021172 |
[16] |
Anna Lisa Amadori. Global bifurcation for the Hénon problem. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4797-4816. doi: 10.3934/cpaa.2020212 |
[17] |
Adnan H. Sabuwala, Doreen De Leon. Particular solution to the Euler-Cauchy equation with polynomial non-homegeneities. Conference Publications, 2011, 2011 (Special) : 1271-1278. doi: 10.3934/proc.2011.2011.1271 |
[18] |
Patricio Felmer, César Torres. Radial symmetry of ground states for a regional fractional Nonlinear Schrödinger Equation. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2395-2406. doi: 10.3934/cpaa.2014.13.2395 |
[19] |
Kaïs Ammari, Thomas Duyckaerts, Armen Shirikyan. Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation. Mathematical Control and Related Fields, 2016, 6 (1) : 1-25. doi: 10.3934/mcrf.2016.6.1 |
[20] |
Yingshu Lü. Symmetry and non-existence of solutions to an integral system. Communications on Pure and Applied Analysis, 2018, 17 (3) : 807-821. doi: 10.3934/cpaa.2018041 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]