The $L_p$ dual Minkowski problem with $p<0<q$ is investigated in this paper. By proving a new existence result of solutions and constructing an example, we obtain the nonuniqueness of solutions to this problem.

中文翻译：

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Lp 对偶闵可夫斯基问题解的非唯一性

本文研究了$p<0<q$的$L_p$对偶Minkowski问题。通过证明解的新存在结果并构造一个例子，我们得到了该问题解的非唯一性。