We consider an anisotropic Dirichlet problem which is driven by the
-Laplacian (that is, the sum of a
-Laplacian and a
-Laplacian), The reaction (source) term, is a Carathéodory function which asymptotically as
can be resonant with respect to the principal eigenvalue of
. First using truncation techniques and the direct method of the calculus of variations, we produce two smooth solutions of constant sign. In fact we show that there exist a smallest positive solution and a biggest negative solution. Then by combining variational tools, with suitable truncation techniques and the theory of critical groups, we show the existence of a nodal (sign changing) solution, located between the two extremal ones.
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