Abstract

We consider positive radially symmetric solutions of -Delta u = lambda(e(u) - 1), in B, u = 0 on partial derivative B, where B is the unit ball in R-N, N >= 3 and lambda > 0 is a parameter. We establish infinite multiplicity of regular solutions for 3 <= N <= 9 and some lambda, and we obtain a bound for the Morse index and the number of solutions when N >= 10. (C) 2013 The Authors. Published by Elsevier Ltd. All rights reserved.