Dirichlet $(p,q)$-equations at resonance

We consider a parametric nonlinear Dirichlet equation driven by the sum of a p-Laplacian and a q-Laplacian ($1 0$ of (-Δₚ, W1,p₀(Ω)). Using critical point theory, truncation and comparison techniques and critical groups (Morse theory), we show that for all small values of the parameter λ>0, the problem has at least five nontrivial solutions, four of constant sign (two positive and two negative) and the fifth nodal (sign-changing).