论文标题
与竞争潜力的关键Kirchhoff方程的正态解决方案的浓度
Concentration of positive ground state solutions for critical Kirchhoff equation with competing potentials
论文作者
论文摘要
在本文中，我们考虑以下奇异扰动的kirchhoff方程\ begin {equation*} - （\ varepsilon^2a+\ varepsilon b \ int b \ int _ {\ mathbb {r}^3} | \ nabla u|^2dx)Δu+V(x)u=P(x)|u|^{p-2}u+Q(x)|u|^4u,\quad x\in\mathbb{R}^3, \end{equation*} where $\varepsilon>0$ is a small parameter, $a, b > 0$ are constants, $p\in(4,6)$ and $ V，P，Q $是满足某些竞争条件的潜在功能。我们通过使用变分方法证明了积极的基态解决方案，并确定了与电势V，p $和$ Q $相关的具体集作为这些基态解决方案的浓度位置为$ \ varepsilon \ to0 $。
In this paper, we consider the following singularly perturbed Kirchhoff equation \begin{equation*} -(\varepsilon^2a+\varepsilon b\int_{\mathbb{R}^3}|\nabla u|^2dx)Δu+V(x)u=P(x)|u|^{p-2}u+Q(x)|u|^4u,\quad x\in\mathbb{R}^3, \end{equation*} where $\varepsilon>0$ is a small parameter, $a, b > 0$ are constants, $p\in(4,6)$ and $V, P, Q$ are potential functions satisfying some competing conditions. We prove the existence of a positive ground state solution by using variational methods, and we determine a concrete set related to the potentials $V,P$ and $Q$ as the concentration position of these ground state solutions as $\varepsilon\to0$.
