论文标题
具有梯度项的加权椭圆系统的径向溶液的存在和边界行为
Existence and boundary behaviour of radial solutions for weighted elliptic systems with gradient terms
论文作者
论文摘要
我们关注系统\ begin {equation*} \ left {\ oken {aligned}Δu＆= | x | x | x |^{a} v^{ u |）&& \ quad \ mbox {in}ω，\ end {Aligned} \ right。 \ end {equation*}其中$ω\ subset \ br^n $要么是以原点为中心的球，要么是整个空间$ \ br^n $，$ a $，$ a $，$ b $，$ p $，$ q> 0 $，$ q> 0 $，而$ f \ in C^1 [0，\ infty）$ a $ f（t）$ f（t）$ f（t）$ t（t）$ t $ t> 0 $ t> 0 $ t> 0 $ t> 0。首先，我们研究了阳性径向溶液的存在，以防系统呈现在与它们在边界处的行为相对应的球中。接下来，我们采用$ f（t）= t^s $，$ s> 1 $，$ω= \ br^n $，并且通过使用动力学系统技术，我们能够描述无限的行为，用于这种正径向解决方案。
We are concerned with the existence and boundary behaviour of positive radial solutions for the system \begin{equation*} \left\{ \begin{aligned} Δu&=|x|^{a}v^{p} &&\quad\mbox{ in } Ω, \\ Δv&=|x|^{b}v^{q}f(|\nabla u|) &&\quad\mbox{ in } Ω, \end{aligned} \right. \end{equation*} where $Ω\subset \bR^N$ is either a ball centered at the origin or the whole space $\bR^N$, $a$, $b$, $p$, $q> 0$, and $f \in C^1[0, \infty)$ is an increasing function such that $f(t)> 0$ for all $t> 0$. Firstly, we study the existence of positive radial solutions in case when the system is posed in a ball corresponding to their behaviour at the boundary. Next, we take $f(t) = t^s$, $s> 1$, $Ω= \bR^N$ and by the use of dynamical system techniques we are able to describe the behaviour at infinity for such positive radial solutions.
