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On the number of maximum points of least energy solution to a two-dimensional Hénon equation with large exponent
Infinite multiplicity for an inhomogeneous supercritical problem in entire space
1. | Department of mathematics, East China Normal University, 500 Dong Chuan Road, Shanghai 200241 |
2. | Department of Mathematics, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong |
References:
[1] |
S. Bae, Infinite multiplicity and separation structure of positive solutions for a semilinear elliptic equation in $\mathbb{R}^{n}$, J. Diff. Eqns., 200 (2004), 274-311.
doi: 10.1016/j.jde.2003.11.006. |
[2] |
G. Bernard, An inhomogeneous semilinear equation in entire space, J. Differential Equations, 125 (1996), 184-214.
doi: 10.1006/jdeq.1996.0029. |
[3] |
S. Bae and W.-M. Ni, Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equationon $R^n$, Math. Ann., 320 (2001), 191-210.
doi: 10.1007/PL00004468. |
[4] |
J. Dávila, M. del Pino and M. Musso, The supercritical Lane-Emden-Fowler equation in exterior domains, Commun. Part. Diff. Equations, 32 (2007), 1225-1243.
doi: 10.1080/03605300600854209. |
[5] |
J. Dávila, M. Del Pino, M. Musso and J. Wei, Standing waves for supercritical nonlinear Schrödinger equations, J. Differential Equations, 236 (2007), 164-198.
doi: 10.1016/j.jde.2007.01.016. |
[6] |
W.-Y. Ding and W.-M. Ni, On the elliptic equation $\Delta u + Ku^{\frac{N + 2}{N - 2}} = 0$ and related topics, Duke Math. J., 52 (1985), 485-506.
doi: 10.1215/S0012-7094-85-05224-X. |
[7] |
C.-F. Gui, Positive entire solutions of equation $\Delta u + f(x, u) = 0$, J. Diff. Eqns., 99 (1992), 245-280.
doi: 10.1016/0022-0396(92)90023-G. |
[8] |
C.-F. Gui, On positive entire solutions of the elliptic equation $\Delta u+K(x) u^p=0$ and its applications to Riemannian geometry, Proc. Roy. Soc. Edinburgh Sect. A, 126 (1996), 225-237.
doi: 10.1017/S0308210500022708. |
[9] |
C.-F. Gui, W.-M. Ni and X. Wang, On the stability and instability of positive steady states of a semilinear heat euqation in $R^N$, Comm. Pure Appl. Math., 45 (1992), 1153-1181.
doi: 10.1002/cpa.3160450906. |
[10] |
Y. Li, Asymptotic behavior of positive solutions of equation $\Delta u+ K(x) u^p=0$ in $R^n$, J. Differential Equations, 95 (1992), 304-330.
doi: 10.1016/0022-0396(92)90034-K. |
[11] |
X.-F. Wang and J.-C. Wei, On the equation $\Delta u +Ku^{\frac{N+ 2}{N - 2} \pm \epsilon^2} = 0$ in $R^n$, Rend. Circ. Mat. Palermo, 44 (1995), 365-400.
doi: 10.1007/BF02844676. |
[12] |
E. Yanagida and S. Yotsutani, Classification of the structure of positive radial solutions to $\Delta u + K(|x|) u^p=0$ in $R^n$, Arch. Rational Mech. Anal., 124 (1993), 239-259.
doi: 10.1007/BF00953068. |
show all references
References:
[1] |
S. Bae, Infinite multiplicity and separation structure of positive solutions for a semilinear elliptic equation in $\mathbb{R}^{n}$, J. Diff. Eqns., 200 (2004), 274-311.
doi: 10.1016/j.jde.2003.11.006. |
[2] |
G. Bernard, An inhomogeneous semilinear equation in entire space, J. Differential Equations, 125 (1996), 184-214.
doi: 10.1006/jdeq.1996.0029. |
[3] |
S. Bae and W.-M. Ni, Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equationon $R^n$, Math. Ann., 320 (2001), 191-210.
doi: 10.1007/PL00004468. |
[4] |
J. Dávila, M. del Pino and M. Musso, The supercritical Lane-Emden-Fowler equation in exterior domains, Commun. Part. Diff. Equations, 32 (2007), 1225-1243.
doi: 10.1080/03605300600854209. |
[5] |
J. Dávila, M. Del Pino, M. Musso and J. Wei, Standing waves for supercritical nonlinear Schrödinger equations, J. Differential Equations, 236 (2007), 164-198.
doi: 10.1016/j.jde.2007.01.016. |
[6] |
W.-Y. Ding and W.-M. Ni, On the elliptic equation $\Delta u + Ku^{\frac{N + 2}{N - 2}} = 0$ and related topics, Duke Math. J., 52 (1985), 485-506.
doi: 10.1215/S0012-7094-85-05224-X. |
[7] |
C.-F. Gui, Positive entire solutions of equation $\Delta u + f(x, u) = 0$, J. Diff. Eqns., 99 (1992), 245-280.
doi: 10.1016/0022-0396(92)90023-G. |
[8] |
C.-F. Gui, On positive entire solutions of the elliptic equation $\Delta u+K(x) u^p=0$ and its applications to Riemannian geometry, Proc. Roy. Soc. Edinburgh Sect. A, 126 (1996), 225-237.
doi: 10.1017/S0308210500022708. |
[9] |
C.-F. Gui, W.-M. Ni and X. Wang, On the stability and instability of positive steady states of a semilinear heat euqation in $R^N$, Comm. Pure Appl. Math., 45 (1992), 1153-1181.
doi: 10.1002/cpa.3160450906. |
[10] |
Y. Li, Asymptotic behavior of positive solutions of equation $\Delta u+ K(x) u^p=0$ in $R^n$, J. Differential Equations, 95 (1992), 304-330.
doi: 10.1016/0022-0396(92)90034-K. |
[11] |
X.-F. Wang and J.-C. Wei, On the equation $\Delta u +Ku^{\frac{N+ 2}{N - 2} \pm \epsilon^2} = 0$ in $R^n$, Rend. Circ. Mat. Palermo, 44 (1995), 365-400.
doi: 10.1007/BF02844676. |
[12] |
E. Yanagida and S. Yotsutani, Classification of the structure of positive radial solutions to $\Delta u + K(|x|) u^p=0$ in $R^n$, Arch. Rational Mech. Anal., 124 (1993), 239-259.
doi: 10.1007/BF00953068. |
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