Solutions of superlinear at zero elliptic equations via Morse theory

(1) { −∆u = f(u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R is an open bounded domain with smooth boundary. We assume that f ∈ C(R,R) satisfies f(0) = 0, so the constant function u ≡ 0 is a trivial solution of (1). We are interested in the existence of nontrivial solutions when f is superlinear at zero, that is near zero it looks like O(u|u|ν−2) for some ν ∈ (1, 2). More precisely, we assume that f and its primitive