We consider the existence of multiple solutions of the following singular nonlocal elliptic problem: $$\begin{aligned} \textstyle\begin{cases} -M(\int _{\mathbb{R} ^{N}}{ \vert x \vert ^{-ap} \vert \nabla u \vert ^{p}})\operatorname{div}( \vert x \vert ^{-ap} \vert \nabla u \vert ^{p-2}\nabla u)= h(x) \vert u \vert ^{r-2}u+H(x) \vert u \vert ^{q-2}u, \\ u(x)\rightarrow 0 \quad \text{as } \vert x \vert \rightarrow \infty , \end{cases}\displaystyle \end{aligned}$$ where $x\in \mathbb{R} ^{N}$, and $M(t)=\alpha +\beta t$. By the variational method we prove that the problem has infinitely many solutions when some conditions are fulfilled.

中文翻译：

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RN中p -Kirchhoff问题的无穷多个解的存在

我们考虑存在以下奇异非局部椭圆问题的多种解决方案：$$ \ begin {aligned} \ textstyle \ begin {cases} -M（\ int _ {\ mathbb {R} ^ {N}} {\ vert x \ vert ^ {-ap} \ vert \ nabla u \ vert ^ {p}}）\操作员名称{div}（\ vert x \ vert ^ {-ap} \ vert \ nabla u \ vert ^ {p-2} \ nabla u）= h（x）\ vert u \ vert ^ {r-2} u + H（x）\ vert u \ vert ^ {q-2} u，\\ u（x）\ rightarrow 0 \ quad \文字{as} \ vert x \ vert \ rightarrow \ infty，\ end {cases} \ displaystyle \ end {aligned} $$其中$ x \ in \ mathbb {R} ^ {N} $和$ M（t） = \ alpha + \ beta t $。通过变分方法，我们证明了当满足某些条件时，该问题具有无限多个解决方案。