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Existence and asymptotic behavior of positive solutions for fractional Kirchhoff type problems with steep potential well
  • Ling Huang,
  • li wang,
  • shenghao Feng
Ling Huang
East China JiaoTong University
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li wang
East China JiaoTong University

Corresponding Author:[email protected]

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shenghao Feng
East China JiaoTong University
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Abstract

\begin{abstract} {In this paper we consider the following fractional Kirchhoff equation with steep potential well \begin{align*} \renewcommand{\arraystretch}{1.25} \begin{array}{ll} \ds \left \{ \begin{array}{ll} \ds \left(a+b\int_{\R^{3}}|(-\Delta)^\frac{s}{2}u|^2\, dx\right)(-\Delta)^s u+\lambda V(x)u=|u|^{p-2}u,\,\,x\in\mathbb{R}^3, \\ u\in H^s(\R^3), \\ \end{array} \right . \end{array} \end{align*} where $a>0$ is a constant, $b$ and $\lambda$ are positive parameters. $2