1. Ground states of a prescribed mean curvature equation
- Author
-
del Pino, Manuel and Guerra, Ignacio
- Subjects
- *
DIFFERENTIAL equations , *MATHEMATICAL physics , *PARTIAL differential equations , *MECHANICS (Physics) - Abstract
Abstract: We study the existence of radial ground state solutions for the problem , . It is known that this problem has infinitely many ground states when , while no solutions exist if . A question raised by Ni and Serrin in [W.-M. Ni, J. Serrin, Existence and non-existence theorems for ground states for quasilinear partial differential equations, Atti Convegni Lincei 77 (1985) 231–257] is whether or not ground state solutions exist for . In this paper we prove the existence of a large, finite number of ground states with fast decay as provided that q lies below but close enough to the critical exponent . These solutions develop a bubble-tower profile as q approaches the critical exponent. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF