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We show that if $V(|x|)$ has the following expansion: \\[ V(|x|)=V_0 + \\frac{a}{|x|^m} + o\\left(\\frac{1}{|x|^m}\\right) \\qquad \\mbox{as} \\ |x| \\rightarrow +\\infty, \\] in which the constants are properly assumed, then (\\ref{abstract}) admits infinitely many non-radial solutions, whose energy can be made arbitrarily large. 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We show that if $V(|x|)$ has the following expansion: \\[ V(|x|)=V_0 + \\frac{a}{|x|^m} + o\\left(\\frac{1}{|x|^m}\\right) \\qquad \\mbox{as} \\ |x| \\rightarrow +\\infty, \\] in which the constants are properly assumed, then (\\ref{abstract}) admits infinitely many non-radial solutions, whose energy can be made arbitrarily large. 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