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We assume that the nonlinearities $f, g$ have critical growth at $+\\infty$ in the sense of Trudinger-Moser inequality and the nonnegative weights $P(x)$ and $Q(x)$ vanish at $+\\infty$. 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We assume that the nonlinearities $f, g$ have critical growth at $+\\infty$ in the sense of Trudinger-Moser inequality and the nonnegative weights $P(x)$ and $Q(x)$ vanish at $+\\infty$. 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