论文标题
涉及单数和指数非线性的分数Kirchhoff问题的Nehari歧管方法
The Nehari manifold method for Fractional Kirchhoff problem involving singular and exponential nonlinearity
论文作者
论文摘要
在本文中，我们确定了至少两个弱解决方案的存在，以解决以下分数Kirchhoff问题，涉及单数和指数非线性\ Begin {equation*} \ left \ {\ begin {split} m \ left（\ | U \ |^{\ frac {n} {s}}} \ right）（ - δ） u＆> 0，\; \ text {in} \; \ om， u＆= 0，\; \ text {in} \; \ mb r^n \ setMinus {\ om}， \ end {split} \正确的。 \ end {equation*}其中$ \ om $是$ \ mb r^n $，{$ n \ geq 1 $}中的平滑界面域，$ s \ in（0,1）$，$μ> 0 $是一个真实参数，$β<\ frac {n} n} {n-s-s} {n-s} $ q \ q \ in（0,1）。我们在这里考虑了退化的Kirchhoff案例，并使用Nehari歧管技术来获得结果。
In this paper we establish the existence of at least two weak solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearity \begin{equation*} \left\{\begin{split} M\left(\|u\|^{\frac{n}{s}}\right)(-Δ)^s_{n/s}u & = μu^{-q}+ u^{r-1}\exp( u^β)\;\text{in}\;\Om, u&>0,\;\text{in}\; \Om, u &= 0,\;\text{in}\; \mb R^n \setminus{\Om}, \end{split} \right. \end{equation*} where $\Om$ is smooth bounded domain in $\mb R^n$, {$n\geq 1$}, $s\in (0,1)$, $μ>0$ is a real parameter, $β<\frac{n}{n-s}$ and $q\in (0,1)$. We have considered the degenerate Kirchhoff case here and used the Nehari manifold techniques to obtain the results.
