In this paper, we study the existence of least energy solutions to the following fractional Kirchhoff problem with logarithmic nonlinearity $\left\{\begin{array}{cc}M\left({\left[u\right]}_{s,p}^p\right){(-\Delta )}_p^{s}u=h\left(x\right){\left|u\right|}^{\theta p-2}uln\left|u\right|+\lambda {\left|u\right|}^{q-2}u\hfill & x\in \Omega ,\hfill \\ u=0\hfill & x\in {\mathbb{R}}^N\setminus \Omega ,\hfill \end{array}\right.$where $s\in$(0,1), $1<p<N∕s$, $\Omega \subset {\mathbb{R}}^N$ is a bounded domain with Lipschitz boundary, $M\left({\left[u\right]}_{s,p}^p\right)={\left[u\right]}_{s,p}^{(\theta -1)p}$ with $\theta \ge 1$ and ${\left[u\right]}_{s,p}$ is the Gagliardo seminorm of $u$, $h\in C\left(\overline{\Omega }\right)$ may change sign, $\lambda >0$ is a parameter, $q\in (1,p_s^{\ast })$ and ${(-\Delta )}_p^s$ is the fractional $p-$Laplacian. When $\theta p<q<p_s^{\ast }$ and $h$ is a positive function on $\Omega$, the existence of least energy solutions is obtained by restricting the discussion on Nehari manifold. When $1<q<\theta p$ and $h$ is a sign-changing function on $\Omega$, two local least energy solutions are obtained by using the Nehari manifold approach.

在本文中，我们研究具有对数非线性的以下分数阶Kirchhoff问题的最小能量解的存在性 $\left\{\begin{array}{cc}\mathrm{中号}（{\left[ü\right]}_{s，p}^p）{（-\Delta ）}_p^sü=H（X）{\left|ü\right|}^{\theta p-2}üln\left|ü\right|+\lambda {\left|ü\right|}^{q-2}ü\hfill & X\in \Omega ，\hfill \\ ü=0\hfill & X\in {\mathbb{[R}}^{ñ}\setminus \Omega ，\hfill \end{array}\right.$哪里 $s\in$（0,1）， $\mathrm{1个}<p<ñ∕s$， $\Omega \subset {\mathbb{[R}}^{ñ}$ 是具有Lipschitz边界的有界域， $\mathrm{中号}（{\left[ü\right]}_{s，p}^p）={\left[ü\right]}_{s，p}^{（\theta -\mathrm{1个}）p}$ 与 $\theta \ge \mathrm{1个}$ 和 ${\left[ü\right]}_{s，p}$ 是Gagliardo的半范数 $ü$， $H\in C（\overline{\Omega }）$ 可能会改变符号 $\lambda >0$ 是一个参数， $q\in （\mathrm{1个}，p_s^{\ast }）$ 和 ${（-\Delta ）}_p^s$ 是分数 $p-$拉普拉斯人。什么时候$\theta p<q<p_s^{\ast }$ 和 $H$ 对...起积极作用 $\Omega$，通过限制关于Nehari流形的讨论，获得了最小能量解的存在。什么时候$\mathrm{1个}<q<\theta p$ 和 $H$ 是在 $\Omega$，通过使用Nehari流形方法获得了两个局部最小能量解。