论文标题
对于线性扰动的关键车道填充系统的解决方案的非固定性
Non-degeneracy of solution for critical Lane-Emden systems with linear perturbation
论文作者
论文摘要
在本文中，我们考虑以下椭圆系统\ begin {equation*} \ begin {case}-ΔU= | v |^{p-1} v +ε（αu +β_1v），＆\ hbox {in}ω，\ \ \ \ \ \ \ \ - ΔV= | U | U | U |^{Q-1} u + + + + + +ε（β） }Ω, \\u=v=0,&\hbox{ on }\partialΩ, \end{cases} \end{equation*} where $Ω$ is a smooth bounded domain in $\mathbb{R}^{N}$, $N\geq 3$, $ε$ is a small parameter, $α$, $ β_1$ and $ β_2$ are实际数字，$（p，q）$是一对位于关键双曲线\ begin {equation*} \ begin {split} \ frac {1} {p+1}+\ frac {1} {q+1} = \ frac {n-2} {n} {n} {n} {n} {n}。 \ end {split} \ end {equation*}我们首先重新审视了在\ cite {kim-pis}中构建的吹式解决方案，然后我们证明了其非降低性。我们认为，我们在本文中使用的各种新思想和技术计算对于处理涉及关键Halmitonian系统和新解决方案的其他相关问题非常有用。
In this paper, we consider the following elliptic system \begin{equation*} \begin{cases} -Δu = |v|^{p-1}v +ε(αu + β_1 v), &\hbox{ in }Ω, \\-Δv = |u|^{q-1}u+ε(β_2 u +αv), &\hbox{ in }Ω, \\u=v=0,&\hbox{ on }\partialΩ, \end{cases} \end{equation*} where $Ω$ is a smooth bounded domain in $\mathbb{R}^{N}$, $N\geq 3$, $ε$ is a small parameter, $α$, $ β_1$ and $ β_2$ are real numbers, $(p,q)$ is a pair of positive numbers lying on the critical hyperbola \begin{equation*} \begin{split} \frac{1}{p+1}+\frac{1}{q+1} =\frac{N-2}{N}. \end{split} \end{equation*} We first revisited the blowing-up solutions constructed in \cite{Kim-Pis} and then we proved its non-degeneracy. We believe that the various new ideas and technique computations that we used in this paper would be very useful to deal with other related problems involving critical Halmitonian system and the construction of new solutions.
