Geodesic
On local unsolvability of differential equations with weighted derivatives
Sbornik. Mathematics, Tome 39 (1981) no. 3, pp. 417-428

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In this paper a local unsolvability theorem is proved for differential equations with weighted derivatives that generalize the class of equations of principal type. In contrast to the latter, here the lower terms have an essential influence on local solvability. In this paper a one-parameter family of hamiltonians is constructed that plays the same role as the principal symbol for equations of principal type, and conditions on the behavior of this family are indicated under which there is no local solvability. Bibliography: 6 titles. 
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     author = {N. A. Shananin},
     title = {On local unsolvability of differential equations with weighted derivatives},
     journal = {Sbornik. Mathematics},
     pages = {417--428},
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     volume = {39},
     number = {3},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_39_3_a6/}
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N. A. Shananin. On local unsolvability of differential equations with weighted derivatives. Sbornik. Mathematics, Tome 39 (1981) no. 3, pp. 417-428. http://geodesic.mathdoc.fr/item/SM_1981_39_3_a6/