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We provide two existence results for sign-changing solutions to the Dirichlet problem for the family of equations −Δpu−Δqu = α |u|p−2u+β |u|q−2u , where 1 < q < p and α , β are parameters. First, we show the existence in the resonant case α ∈ σ(−Δp) for sufficiently large β , thereby generalizing previously known results. The obtained solutions have negative energy. Second, we show the existence for any β λ1(q) and sufficiently large α under an additional nonresonant assumption, where λ1(q) is the first eigenvalue of the q -Laplacian. The obtained solutions have positive energy.

On sign-changing solutions for resonant (p,q)-Laplace equations