Ground state solutions for the Hénon prescribed mean curvature equation

Advances in Nonlinear Analysis

article

Antonio Azzollini¹ 

[1] Dipartimento di Matematica, Università degli Studi della Basilicata

关键词: Quasilinear elliptic equations;    mean curvature operator;    ODEs techniques;   

DOI  :  10.1515/anona-2017-0233

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we consider the analogous of the Hénon equation for the prescribed mean curvature problem in ℝ N {{\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.

【 授权许可】

CC BY