The small parameter method for regular linear differential equations on unbounded domains

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.