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bounded domain in $\\mathbb{R}^N$, $N \\geq 3$, while $\\Delta_\\gamma$ is the Grushin operator $$ \\Delta_ \\gamma u(z) = \\Delta_x u(z) + \\vert x \\vert^{2\\gamma} \\Delta_y u (z) \\quad (\\gamma\\ge 0). $$ We prove a multiplicity and bifurcation result for this problem, extending the results of Cerami, Fortunato and Struwe and of Fiscella, Molica Bisci and 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