Existence of solutions for a higher order Kirchhoff type problem with exponential critical growth

The higher order Kirchhoff type equation $${\int }_{{\mathbb{R}}^{2m}}(\mathrm{\mid }{\mathrm{\nabla }}^{m}u{\mathrm{\mid }}^2+\sum _{\gamma =0}^{m-1}{a}_{\gamma }(x)\mathrm{\mid }{\mathrm{\nabla }}^{\gamma }u{\mathrm{\mid }}^2)dx((-\mathrm{\Delta }{)}^{m}u+\sum _{\gamma =0}^{m-1}(-1{)}^{\gamma }{\mathrm{\nabla }}^{\gamma }\cdot (a_{\gamma }(x){\mathrm{\nabla }}^{\gamma }u))=\frac{f(x,u)}{\mathrm{\mid }x{\mathrm{\mid }}^{\beta }}+ϵh(x)\text{ in }{\mathbb{R}}^{2m}$$ is considered in this paper. We assume that the nonlinearity of the equation has exponential critical growth and prove that, for a positive $ϵ$ which is small enough, there are two distinct nontrivial solutions to the equation. When $ϵ=0$, we also prove that the equation has a nontrivial mountain-pass type solution.