Geodesic
The small parameter method for regular linear differential equations on unbounded domains
Eurasian mathematical journal, Tome 4 (2013) no. 2, pp. 64-81.

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Algorithms for the asymptotic expansion of the solution to the Dirichlet problem for a regular equation with a small parameter $\varepsilon$ ($\varepsilon>0$) at higher derivatives on an unbounded domain (the whole space, the half space and a strip), based on the solution to the degenerate (as $\varepsilon\to0$) Dirichlet problem for a regular hypoelliptic equation of the lower order, are described. Estimates for remainder terms of those expansions are obtained. 
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G. A. Karapetyan; H. G. Tananyan. The small parameter method for regular linear differential equations on unbounded domains. Eurasian mathematical journal, Tome 4 (2013) no. 2, pp. 64-81. http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a4/

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