论文标题
多功能解决方案，用于稍微亚临界椭圆形问题，非电力非线性
Multispike Solutions for a slightly subcritical elliptic problem with non-power nonlinearity
论文作者
论文摘要
在本文中，我们关注以下椭圆方程$$ \ weft \ {\ begin {array} {rrl} {rrl}-ΔU＆=＆| U | |^{4/（n-2）} u/[\ ln（e+| U |）]^\ varepsilon \ hbox { ω，\ end {array} \ right。$$，其中$ω$是$ \ mathbb {r}^n，\ n \ geq 3 $和$ \ varepsilon> 0 $中的平滑有限的开放域。 Clapp等。在《差异杂志》中。等式。 （第275卷）证明，如果$ n \ geq 4 $，则存在一个单峰阳性解决方案。在这里，我们构建正面和更改符号解决方案同时集中在几个点上。
In this paper, we are concerned with the following elliptic equation $$\left\{\begin{array}{rrl}-Δu&=& |u|^{4/(n-2)}u/[\ln (e+|u|)]^\varepsilon\hbox{ in } Ω,\\ u&=&0 \hbox{ on }\partial Ω, \end{array} \right.$$ where $Ω$ is a smooth bounded open domain in $\mathbb{R}^n, \ n\geq 3$ and $\varepsilon>0$. Clapp et al. in Journal of Diff. Eq. (Vol 275) proved that there exists a single-peak positive solution for small $\varepsilon$ if $n \geq 4$. Here we construct positive as well as changing sign solutions concentrated at several points at the same time.
