On ground state of fractional $p$-Kirchhoff equation involving subcritical and critical exponential growth

On ground state of fractional $p$-Kirchhoff equation involving subcritical and critical exponential growth

In this paper, we concern the existence of nontrivial ground state solutions offractional $p$-Kirchhoff equation$$left{begin{array}{ll}mleft(|u|^pright) [(-Delta)_p^su+V(x)|u|^{p-2}u]=f(x,u) quadtext{in}, mathbb{R}^N, vspace{0.2cm} |u|=left(int_{mathbb{R}^{2N}}frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy +int_{mathbb{R}^N}V(x)|u|^pdxright)^{frac{1}{p}},end{array}right.$$where $m:[0,+infty)rightarrow [0,+infty)$ is a continuous function, $(-Delta)_p^s$ is the fractional $p$-Laplacian operator with $0