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A Dirichlet problem driven by the $(p,q)$-Laplace operator and an asymmetricconcave reaction with positive parameter is investigated. Four nontrivialsmooth solutions (two positive, one negative, and the remaining nodal) areobtained once the parameter turns out to be sufficiently small. Under a oddnesscondition near the origin for the perturbation, a whole sequence ofsign-changing solutions, which converges to zero, is produced.

On a $(p,q)$-Laplacian problem with parametric concave term and asymmetric perturbation