Ground state solutions for the Hénon prescribed mean curvature equation
In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in ℝN{{\mathbb{R}^{N}}}, both in the Euclidean and in the Minkowski spaces. Motivated by the studies of Ni and Serrin [W. M. Ni and J. Serrin, Existence and non-existence theorems for ground stat...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-06-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2017-0233 |
| Summary: | In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in ℝN{{\mathbb{R}^{N}}}, both in the Euclidean and in the Minkowski spaces. Motivated by the studies of Ni and Serrin [W. M. Ni and J. Serrin,
Existence and non-existence theorems for ground states for quasilinear partial differential equations,
Att. Convegni Lincei 77 1985, 231–257], we have been interested in finding the relations between the growth of the potential and that of the local nonlinearity in order to prove the nonexistence of a radial ground state. We also present a partial result on the existence of a ground state solution in the Minkowski space. |
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| ISSN: | 2191-9496 2191-950X |