Categoricity of an abstract elementary class in two cardinals

We investigate categoricity of abstract elementary classes without any remnants of compactness (like non-definability of well ordering, existence of E.M. models, or existence of large cardinals). We prove (assuming a weak version of GCH around λ) that if A is categorical in λ, λ⁺, LS(ℛ) ≤ λ and has intermediate number of models in λ⁺⁺, then ℛ has a model in λ⁺⁺⁺.