论文标题
某些混合阶椭圆系统的解决方案分类
Classification of solutions for some mixed order elliptic system
论文作者
论文摘要
在本文中，我们将以下混合订单的解决方案与$ \ Mathbb {r}^4 $：\ begin {equation} \ left \ left \ okent {aligned}＆-ΔU（x）= u^{p_1}（p_1} e^e^e^q^q^q^q^q^q^q^q. \ Mathbb {r}^4，\\＆（-Δ）^2 V（x）= u^{p_2}（x） \ end {equation}其中$ 0 \ leq p_1 <1 $，$ p_2> 0 $，$ q_1> 0 $，$ q_2 \ geq 0 $，$ u> 0 $，并满足$ \ int \ int _ {\ mathbb {r} \ int _ {\ mathbb {r}^4} u^{p_2}（x）e^{q_2 v（x）} dx <\ infty。通过使用移动球的方法，我们获得了系统中解决方案的分类结果。
In this paper, we classify the solution of the following mixed-order conformally invariant system with coupled nonlinearity in $ \mathbb{R}^4$: \begin{equation}\left\{ \begin{aligned} & -Δu(x) = u^{p_1}(x) e^{q_1v(x)}, \quad x\in \mathbb{R}^4,\\ & (-Δ)^2 v(x) = u^{p_2}(x) e^{q_2v(x)}, \quad x\in \mathbb{R}^4, \end{aligned} \right. \end{equation} where $ 0\leq p_1 < 1$, $ p_2 >0$, $ q_1 > 0$, $ q_2 \geq 0$, $ u>0$ and satisfies $$ \int_{\mathbb{R}^4} u^{p_1}(x) e^{q_1v(x)} dx < \infty,\quad \int_{\mathbb{R}^4} u^{p_2}(x) e^{q_2 v(x)} dx < \infty.$$ Under additional assumptions (H1) or (H2), we study the asymptotic behavior of the solutions to the system and we establish the equivalent integral formula for the system. By using the method of moving spheres, we obtain the classification results of the solutions in the system.
