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In the case $n\\geq 3$ we use variational methods to prove that for all $p\\in (\\frac{n}{n-2},\\frac{n}{n-2}+\\eps)$ there exist distributional solutions with a point singularity at the origin provided $\\eps>0$ is sufficiently small and $V,\\Gamma$ are bounded on $\\R^n\\setminus B_1(0)$ and satisfy suitable H\\\"{o}lder-type conditions at the origin. 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