Resonance phenomenon for a Gelfand-type problem

We consider positive radially symmetric solutions of −Δu=λ(eu−1),inB,u=0on  ∂B, where B is the unit ball in RN, N≥3 and λ>0 is a parameter. We establish infinite multiplicity of regular solutions for 3≤N≤9 and some λ, and we obtain a bound for the Morse index and the number of solutions when N≥10.