Three solutions for parametric problems with nonhomogeneous (a,2)-type differential operators and reaction terms sublinear at zero

We consider parametric Dirichlet problems driven by the sum of a Laplacian and a nonhomogeneous differential operator ((a,2)-type equation) and with a reaction term which exhibits arbitrary polynomial growth and a nonlinear dependence on the parameter. We prove the existence of three distinct nontrivial smooth solutions for small values of the parameter, providing sign information for them: one is positive, one is negative and the third one is nodal