Affiliation:
1. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Via dell’Ateneo Lucano 10, 85100 Potenza, Italy
Abstract
Abstract
In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in
{{\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.
Cited by
1 articles.
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