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We establish a lower and upper solutions' method to show the existence of a smooth positive solution for the equation (EQ1) \\begin{equation}\n  \\label{E4} \\Delta u \\ + \\ a(x)u \\ = \\ f(x)F(u) \\ + \\ h(x)H(u), (EQ1) \\end{equation} where \\ $a, \\ f, \\ h$ \\ are positive smooth functions on $M^n$, a $n-$dimensional compact Riemannian manifold, and \\ $ F, \\ H$ \\ are non-decreasing smooth functions on $\\mathbb{R}$. 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