Asymptotic behavior at infinity of the Dirichlet problem solution of the $2k$ order equation in a layer

For the operator $(-\Delta)^{k} u(x)+\nu^{2k}u(x)$ with $x \in R^{n} (n\geqslant 2 , k\geqslant 2)$ an explicit fundamental solution is obtained, and for the equation $(- \Delta)^{k} u(x)+\nu^{2k}u(x)=f(x)$ (for $f\in C^{\infty}(R^{n})$ with compact support) the leading term of an asymptotic expansion at infinity of a solution is computed. The same result is obtained for the solution of the Dirichlet problem in a layer in $R^{n+1}$.