Geodesic
Asymptotic behavior at infinity of the Dirichlet problem solution of the $2k$ order equation in a layer
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 311-317

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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 $R^{n+1}$.
Keywords: asymptotic behavior, fundamental solution, $G$-Meyer function.
Mots-clés : elliptic equation, estimation of solution 
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     author = {Mikhail S. Kildyushov and Valery A. Nikishkin},
     title = {Asymptotic behavior at infinity of the {Dirichlet} problem solution of the $2k$ order equation in a layer},
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Mikhail S. Kildyushov; Valery A. Nikishkin. Asymptotic behavior at infinity of the Dirichlet problem solution of the $2k$ order equation in a layer. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 311-317. http://geodesic.mathdoc.fr/item/JSFU_2014_7_3_a4/