论文标题
存在关键指数和测量数据的奇异椭圆问题的积极解决方案
Existence of positive solutions for a singular elliptic problem with critical exponent and measure data
论文作者
论文摘要
我们证明存在阳性{\ it sola（解决方案作为近似的限制）}}以下PDE，涉及laplacian的分数力量 \ begin {equation} \ begin {split} （-Δ）^su＆= \ frac {1} {u^γ}+λu^{2_s^* - 1}+μ〜 \ text {in} 〜Ω，u＆> 0〜 \ text {in} 〜Ω \ end {split} \ end {equation}在这里，$ω$是$ \ mathbb {r}^n $，$ s \ in（0,1）$，$ 2S <n $，$λ，γ\ in（0,1）$，$ 2_S $，$ 2_S^*= \ frac {2n} $ IS $ frac {n-2s $ fracement and s of frac frace and so frac frace and， $ω$中的非负界ra。
We prove the existence of a positive {\it SOLA (Solutions Obtained as Limits of Approximations)} to the following PDE involving fractional power of Laplacian \begin{equation} \begin{split} (-Δ)^su&= \frac{1}{u^γ}+λu^{2_s^*-1}+μ~\text{in}~Ω, u&>0~\text{in}~Ω, u&= 0~\text{in}~\mathbb{R}^N\setminusΩ. \end{split} \end{equation} Here, $Ω$ is a bounded domain of $\mathbb{R}^N$, $s\in (0,1)$, $2s<N$, $λ,γ\in (0,1)$, $2_s^*=\frac{2N}{N-2s}$ is the fractional critical Sobolev exponent and $μ$ is a nonnegative bounded Radon measure in $Ω$.
