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

Corresponding Author:[email protected]

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shenghao Feng
East China Jiao Tong University
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Abstract

{We study the existence and asymptotic behavior of positive solutions for the following fractional magnetic 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)_A^\frac{s}{2}u|^2\, dx\right)(-\Delta)_A^s u+V_{\lambda}u=|u|^{p-2}u~~~in~\mathbb{R}^3, \\ u\in H^s(\R^3), \\ \end{array} \right . \end{array} \end{align*} where $a,~b>0$ are constants, $2