Geodesic
The maximal nonuniqueness classes of solutions to the Cauchy problem for linear equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 90-93

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We study linear partial differential equations with increasing coefficients in a half-plane. We establish maximal nonuniqueness classes of solutions to the Cauchy problem for these equations. The proof is based on a new estimation method for a solution to the dual differential equation with a parameter.
Keywords: classes of uniqueness and nonuniqueness, Newton's diagram, Cauchy problem. 
D. V. Turtin. The maximal nonuniqueness classes of solutions to the Cauchy problem for linear equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 90-93. http://geodesic.mathdoc.fr/item/IVM_2010_9_a9/
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[1] Chebotarev N. G., Teoriya algebraicheskikh funktsii, Gostekhizdat, M., 1948

[2] Kosarev N. G., “O edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s peremennymi koeffitsientami”, Kachestvennye i priblizhennye metody issledovaniya operatornykh uravnenii, 2, Yaroslavl, 1977, 141–158 | MR | Zbl

[3] Gelfand I. M., Shilov G. E., Obobschennye funktsii. Nekotorye voprosy teorii differentsialnykh uravnenii, Fizmatlit, M., 1958 | MR

[4] Zhitomirskii Ya. I., “Klassy edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s rastuschimi koeffitsientami”, Izv. AN SSSR. Ser. matem., 31:4 (1967), 763–782 | MR | Zbl

[5] Kosarev N. G., “O zadache Koshi dlya lineinykh uravnenii s peremennymi koeffitsientami”, Nauchnye trudy IvGU. Matematika, 2, Ivanovo, 1999, 86–92

[6] Zolotarev G. N., “Netrivialnye resheniya zadachi Koshi s nulevymi nachalnymi usloviyami”, Uchen. zap. Ivanovsk. gos. ped. in-ta, 31 (1963), 29–36 | MR