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If $M$ supports a proper isoparametric function with focal varieties $M_1$, $M_2$ of dimension $d_1 \\geq d_2 $ we show that for any $q<\\frac{ n-d_2+2 }{n - d_2 -2}$ the number of positive solutions of the equation $-\\Delta_g u + \\lambda u = \\lambda u^q$ tends to $\\infty$ as $\\lambda \\rightarrow +\\infty$. 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