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\centerline{\scshape Michael Filippakis\footnote{The publication of this paper has been partly supported by the University of Piraeus Research Center}}
{\footnotesize
\centerline{Department of Digital Systems }
\centerline{Univeristy of Piraeus}
\centerline{Piraeus 18536, Greece}
}
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{\bfseries Abstract.}\footnote{The publication of this paper has been partly supported by the University of Piraeus Research Center}}
We consider a nonlinear nonhomogeneous Robin problem driven by the sum of a $p$-Laplacian and of $q$-Laplacian(a $(p,q)$-equation). The reaction term is a Caratheodory function which is resonant at $\pm\infty$ with respect to any nonprincipal variational eigenvalue of the Robin $p$-Laplacian. Using variational methods together with Morse theory (critical groups), we show the existence of at least three nontrivial smooth solutions.
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