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On the elliptic equation Δu+K up = 0 in $\mathbb{R}$n
1. | Faculty of Liberal Arts and Sciences, Hanbat National University, Daejeon, 305-719 |
References:
[1] |
S. Bae, Positive entire solutions of semilinear elliptic equations with quadratically vanishing coefficient, J. Differential Equations, 237 (2007), 159-197.
doi: 10.1016/j.jde.2007.03.003. |
[2] |
S. Bae, Separation structure of positive radial solutions of a semilinear elliptic equation in $\mathbb{R}^{N}$, J. Differential Equations, 194 (2003), 460-499.
doi: 10.1016/S0022-0396(03)00172-4. |
[3] |
S. Bae and T. K. Chang, On a class of semilinear elliptic equations in $\mathbb{R}^{N}$, J. Differential Equations, 185 (2002), 225-250.
doi: 10.1006/jdeq.2001.4162. |
[4] |
L. A. 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. |
[5] |
W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991), 615-622.
doi: 10.1215/S0012-7094-91-06325-8. |
[6] |
W. Y. Ding and W. M. Ni, On the elliptic equation $\Delta u+Ku^(n+2)/(n-2)=0$ and related topics, Duke Math. J., 52 (1985), 485-506.
doi: 10.1215/S0012-7094-85-05224-X. |
[7] |
R. H. Fowler, Further studies of Emden's and similar differential equations, Quarterly J. Math, 2 (1931), 259-288. |
[8] |
B. Gidas and J. Spruck, Global and local behavior of positive solutions of non-linear elliptic equations, Comm. Pure Appl. Math, 23 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[9] |
R. A. Johnson, X. Pan and Y. Yi, Singular ground states of semilinear elliptic equations via invariant manifold theory, Nonlinear Anal., 20 (1993), 1279-1302.
doi: 10.1016/0362-546X(93)90132-C. |
[10] |
R. A. Johnson, X. Pan and Y. Yi, Positive solutions of super-critical elliptic equations and asymptotics, Comm. Partial Differential Equations, 18 (1993), 977-1019.
doi: 10.1080/03605309308820958. |
[11] |
D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rational Mech. Anal., 49 (1973), 241-269.
doi: 10.1007/BF00250508. |
[12] |
N. Korevaar, R. Mazzeo, F. Pacard and R. Schoen, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math, 135 (1999), 233-272.
doi: 10.1007/s002220050285. |
[13] |
Y. Li, Asymptotic behavior of positive solutions of equation $\Delta u + K(x)u^p=0$ in $\mathbb{R}^{N}$, J. Differential Equations, 95 (1992), 304-330.
doi: 10.1016/0022-0396(92)90034-K. |
[14] |
Y. Li and W. M. Ni, On conformal scalar curvature equation in $\mathbb{R}^{N}$, Duke Math. J., 57 (1988), 895-924.
doi: 10.1215/S0012-7094-88-05740-7. |
[15] |
Y. Liu, Y. Li and Y. Deng, Separation property of solutions for a semilinear elliptic equation, J. Differential Equations, 163 (2000), 381-406.
doi: 10.1006/jdeq.1999.3735. |
[16] |
R. Mazzeo and F. Pacard, Constant scalar curvature metrics with isolated singularities, Duke Math. J., 99 (1999), 353-418.
doi: 10.1215/S0012-7094-99-09913-1. |
[17] |
W. M. Ni, On the elliptic equation $\Delta u +K(x)u^(n+2)/(n-2)=0$, its generalizations, and applications in geometry, Indiana Univ. Math. J., 31 (1982), 493-529.
doi: 10.1512/iumj.1982.31.31040. |
[18] |
W. M. Ni and J. Serrin, Nonexistence theorems for singular solutions of quasilinear partial differential equations, Comm. Pure Appl. Math., 36 (1986), 379-399.
doi: 10.1002/cpa.3160390306. |
[19] |
W. M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics, Japan J. Appl. Math., 5 (1988), 1-32.
doi: 10.1007/BF03167899. |
[20] |
E. Yanagida and S. Yotsutani, Classification of the structure of positive radial solutions to $\Delta u + K(|x|)u^p=0$ in $\mathbb{R}^{N}$, Arch. Rational Mech. Anal., 124 (1993), 239-259.
doi: 10.1007/BF00953068. |
show all references
References:
[1] |
S. Bae, Positive entire solutions of semilinear elliptic equations with quadratically vanishing coefficient, J. Differential Equations, 237 (2007), 159-197.
doi: 10.1016/j.jde.2007.03.003. |
[2] |
S. Bae, Separation structure of positive radial solutions of a semilinear elliptic equation in $\mathbb{R}^{N}$, J. Differential Equations, 194 (2003), 460-499.
doi: 10.1016/S0022-0396(03)00172-4. |
[3] |
S. Bae and T. K. Chang, On a class of semilinear elliptic equations in $\mathbb{R}^{N}$, J. Differential Equations, 185 (2002), 225-250.
doi: 10.1006/jdeq.2001.4162. |
[4] |
L. A. 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. |
[5] |
W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991), 615-622.
doi: 10.1215/S0012-7094-91-06325-8. |
[6] |
W. Y. Ding and W. M. Ni, On the elliptic equation $\Delta u+Ku^(n+2)/(n-2)=0$ and related topics, Duke Math. J., 52 (1985), 485-506.
doi: 10.1215/S0012-7094-85-05224-X. |
[7] |
R. H. Fowler, Further studies of Emden's and similar differential equations, Quarterly J. Math, 2 (1931), 259-288. |
[8] |
B. Gidas and J. Spruck, Global and local behavior of positive solutions of non-linear elliptic equations, Comm. Pure Appl. Math, 23 (1981), 525-598.
doi: 10.1002/cpa.3160340406. |
[9] |
R. A. Johnson, X. Pan and Y. Yi, Singular ground states of semilinear elliptic equations via invariant manifold theory, Nonlinear Anal., 20 (1993), 1279-1302.
doi: 10.1016/0362-546X(93)90132-C. |
[10] |
R. A. Johnson, X. Pan and Y. Yi, Positive solutions of super-critical elliptic equations and asymptotics, Comm. Partial Differential Equations, 18 (1993), 977-1019.
doi: 10.1080/03605309308820958. |
[11] |
D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rational Mech. Anal., 49 (1973), 241-269.
doi: 10.1007/BF00250508. |
[12] |
N. Korevaar, R. Mazzeo, F. Pacard and R. Schoen, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math, 135 (1999), 233-272.
doi: 10.1007/s002220050285. |
[13] |
Y. Li, Asymptotic behavior of positive solutions of equation $\Delta u + K(x)u^p=0$ in $\mathbb{R}^{N}$, J. Differential Equations, 95 (1992), 304-330.
doi: 10.1016/0022-0396(92)90034-K. |
[14] |
Y. Li and W. M. Ni, On conformal scalar curvature equation in $\mathbb{R}^{N}$, Duke Math. J., 57 (1988), 895-924.
doi: 10.1215/S0012-7094-88-05740-7. |
[15] |
Y. Liu, Y. Li and Y. Deng, Separation property of solutions for a semilinear elliptic equation, J. Differential Equations, 163 (2000), 381-406.
doi: 10.1006/jdeq.1999.3735. |
[16] |
R. Mazzeo and F. Pacard, Constant scalar curvature metrics with isolated singularities, Duke Math. J., 99 (1999), 353-418.
doi: 10.1215/S0012-7094-99-09913-1. |
[17] |
W. M. Ni, On the elliptic equation $\Delta u +K(x)u^(n+2)/(n-2)=0$, its generalizations, and applications in geometry, Indiana Univ. Math. J., 31 (1982), 493-529.
doi: 10.1512/iumj.1982.31.31040. |
[18] |
W. M. Ni and J. Serrin, Nonexistence theorems for singular solutions of quasilinear partial differential equations, Comm. Pure Appl. Math., 36 (1986), 379-399.
doi: 10.1002/cpa.3160390306. |
[19] |
W. M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics, Japan J. Appl. Math., 5 (1988), 1-32.
doi: 10.1007/BF03167899. |
[20] |
E. Yanagida and S. Yotsutani, Classification of the structure of positive radial solutions to $\Delta u + K(|x|)u^p=0$ in $\mathbb{R}^{N}$, Arch. Rational Mech. Anal., 124 (1993), 239-259.
doi: 10.1007/BF00953068. |
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