Geodesic
A Method for Constructing Solutions to Linear Systems of Partial Differential Equations
Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 191-204

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We obtain some conditions of solvability in Sobolev spaces for the systems of linear partial differential equations and deduce the corresponding formulas for solutions to these systems. The solutions are given as the sum of the series whose terms are the iterations of some pseudodifferential operators constructed explicitly. 
@article{MT_2006_9_2_a8,
     author = {A. A. Shlapunov},
     title = {A {Method} for {Constructing} {Solutions} to {Linear} {Systems} of {Partial} {Differential} {Equations}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {191--204},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2006_9_2_a8/}
}
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A. A. Shlapunov. A Method for Constructing Solutions to Linear Systems of Partial Differential Equations. Matematičeskie trudy, Tome 9 (2006) no. 2, pp. 191-204. http://geodesic.mathdoc.fr/item/MT_2006_9_2_a8/