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| We consider a nonlinear, nonhomogeneous parametric elliptic Dirichlet equation driven by the sum of a $p$-Laplacian and a Laplacian (so-called $(p,2)$-equation) and with a nonlinearity involving a concave term which enters with a negative sign. By applying variational methods along with truncation and comparison techniques as well as Morse theory, we show that the problem under consideration has at least five nontrivial solutions (four of them have constant sign) for all sufficiently small values of the parameter. |
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