In this paper, we study weak solutions, possibly unbounded and sign-changing, to the double phase problem\begin{equation*}-\text{div} (|\nabla u|^{p-2} \nabla u + w(x)|\nabla u|^{q-2} \nabla u) = \left(\frac{1}{|x|^{N-\mu}}*f|u|^r\right) f(x)|u|^{r-2}u \quad\text{in}\ \mathbb{R}^N,\end{equation*}where $q\ge p\ge2$, r > q, $0 \lt \mu \lt N$ and $w,f \in L^1_{\rm loc}(\mathbb{R}^N)$ are two non-negative functions such that $w(x) \le C_1|x|^a$ and $f(x) \ge C_2|x|^b$ for all $|x| \gt R_0$, where $R_0,C_1,C_2 \gt 0$ and $a,b\in\mathbb{R}$. Under some appropriate assumptions on p, q, r, µ, a, b and N, we prove various Liouville-type theorems for weak solutions which are stable or stable outside a compact set of $\mathbb{R}^N$. First, we establish the standard integral estimates via stability property to derive the non-existence results for stable weak solutions. Then, by means of the Pohožaev identity, we deduce the Liouville-type theorem for weak solutions which are stable outside a compact set.

在本文中，我们研究双相问题的弱解，可能是无界且符号变化的\begin{equation*}-\text{div} (|\纳布拉 u|^{p-2} \纳布拉 u + w(x)|\纳布拉 u|^{q-2} \纳布拉 u) = \left(\frac{1}{|x|^{N-\ mu}}*f|u|^r\right) f(x)|u|^{r-2}u \quad\text{in}\ \mathbb{R}^N,\end{方程*}< /span> 的紧集之外稳定或稳定。首先，我们通过稳定性性质建立标准积分估计，导出稳定弱解的不存在结果。然后，利用Pohožaev恒等式，推导出紧集外稳定弱解的Liouville型定理。$\mathbb{R}^N$，我们证明了各种Liouville-弱解的类型定理，这些解在 N 和 b a>a，μ， 是两个非负函数，使得 , q, p。在一些适当的假设下 $a,b\in\mathbb{R}$ 和 $R_0,C_1,C_2 \gt 0$，其中 $|x| \gt R_0$ 对于所有 $f(x) \ge C_2|x |^b$ 和 $w(x) \le C_1|x|^a$$w,f \in L^1_{\rm loc}(\mathbb{R}^N)$$0 \lt \mu \lt N$ 和 $0 \lt \mu \lt N$、q > > r, $q\ge p\ge2$其中