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We consider a nonlinear elliptic equation driven by the sum of a p-Laplacian and a q-Laplacian, where 1 < q ≤ 2 ≤ p < ∞ with a (p − 1)-superlinear Carathéodory reaction term which doesn't satisfy the usual Ambrosetti-Rabinowitz condition. Using variational methods based on critical point theory together with techniques from Morse theory, we show that the problem has at least three nontrivial solutions; among them one is positive and one is negative.doi:10.1090/s0002-9947-2013-06124-7 fatcat:4yndirixq5esrjytn7jdnpnkyi