Ground state solutions for the Hénon prescribed mean curvature equation

Abstract

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.

Keywords

• quasilinear elliptic equations
• mean curvature operator
• odes techniques
• 35j62
• 35j93
• 35a24