Ground state solutions for the Hénon prescribed mean curvature equation

• Main Author: Azzollini Antonio
• Format: Article
• Language: English
• Published: De Gruyter 2018-06-01
• Series: Advances in Nonlinear Analysis
• Subjects: quasilinear elliptic equations; mean curvature operator; odes techniques; 35j62; 35j93; 35a24
• Online Access: https://doi.org/10.1515/anona-2017-0233

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.