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Examples of this type of PDE arise in the theory of singular ergodic control. We show that there is a unique $\\lambda^*$ for which the above equation has a solution $u$ with appropriate growth as $|x|\\rightarrow \\infty$. 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Examples of this type of PDE arise in the theory of singular ergodic control. We show that there is a unique $\\lambda^*$ for which the above equation has a solution $u$ with appropriate growth as $|x|\\rightarrow \\infty$. 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