Uniqueness theorems for linear non-local problems for abstract differential equations
Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 333-363.

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The paper deals with linear non-local problems for differential equations in Banach spaces. We prove a criterion for uniqueness of solution and obtain some corollaries and generalizations.
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I. V. Tikhonov. Uniqueness theorems for linear non-local problems for abstract differential equations. Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 333-363. http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a5/

[1] Hille E., “The abstract Cauchy problem and Cauchy's problem for parabolic differential equations”, J. d'Analyse Math., 3 (1954), 81–196 | DOI | MR | Zbl

[2] Hille E., “Some aspect of Cauchy's problem”, Proc. Intern. Congr. of Math., V. 3 (Amsterdam, Sept. 2 – Sept. 9, 1954), North-Holland Publ. Co., Amsterdam, 1956, 109–116 | MR

[3] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, IL, M., 1962

[4] Lyubich Yu. I., “K teoreme edinstvennosti resheniya abstraktnoi zadachi Koshi”, UMN, 16:5 (1961), 181–182 | MR | Zbl

[5] Lyubich Yu. I., “Klassicheskoe i lokalnoe preobrazovanie Laplasa v abstraktnoi zadache Koshi”, UMN, 21:3 (1966), 3–51 | Zbl

[6] Ivanov V. K., Melnikova I. V., Filinkov A. I., Differentsialno-operatornye uravneniya i nekorrektnye zadachi, Fizmatlit, M., 1995 | MR

[7] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, IL, M., 1951

[8] Krein S. G., Khazan M. I., “Differentsialnye uravneniya v banakhovom prostranstve”, Itogi nauki i tekhniki. Matematicheskii analiz, 21, VINITI, M., 1983, 130–264 | MR

[9] Shelukhin V. V., “Variatsionnyi printsip v nelokalnykh po vremeni zadachakh dlya lineinykh evolyutsionnykh uravnenii”, Sib. matem. zhurn., 34:2 (1993), 191–207 | MR | Zbl

[10] Dezin A. A., Obschie voprosy teorii granichnykh zadach, Nauka, M., 1980 | MR | Zbl

[11] Vejvoda O. et al., Partial differential equations: time-periodic solutions, Martinus Nijhoff Publishers, The Hague, 1982 | Zbl

[12] Khill E., Funktsionalnyi analiz i polugruppy, IL, M., 1951

[13] Pólya G., “Über die Nullstellen gewisser ganzer Funktionen”, Math. Zeit., 2:3/4 (1918), 352–383 | DOI | MR | Zbl

[14] Titchmarsh E. C., “The zeros of certain integral functions”, Proc. London Math. Soc., 25:4 (1926), 283–302 | DOI | MR | Zbl

[15] Cartwright M. L., “The zeros of certain integral functions”, Quart. J. Math., 1:1 (1930), 38–59 | DOI | MR | Zbl

[16] Sedletskii A. M., Fourier transforms and approximations, Gordon and Breach Science Publishers, Amsterdam, 2000 | MR | Zbl

[17] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR

[18] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[19] Leontev A. F., “O svoistvakh posledovatelnostei polinomov Dirikhle, skhodyaschikhsya na intevale mnimoi osi”, Izv. AN SSSR. Ser. matem., 29:2 (1965), 269–328 | MR | Zbl

[20] Pólya G., “Über ganze Funktionen vom Minimaltypus der Ordnung 1”, Aufgaben und Lösungen. Aufgabe 105, Jahresbericht Deutsch. Math. Vereinigung, 40 (1931), 80; Aufgaben und Lösungen. Lösungen der Aufgabe 105, Ibid., 43 (1933), 10–13 | Zbl

[21] Krein S. G., “O klassakh korrektnosti dlya nekotorykh granichnykh zadach”, DAN SSSR, 114:6 (1957), 1162–1165 | MR | Zbl

[22] Orlovskii D. G., “K zadache opredeleniya parametra evolyutsionnogo uravneniya”, Diff. uravneniya, 26:9 (1990), 1614–1621 | MR

[23] Polia G., Sege G., Zadachi i teoremy iz analiza, Ch. 2, Nauka, M., 1978

[24] Tikhonov I. V., “O razreshimosti zadachi s nelokalnym integralnym usloviem dlya differentsialnogo uravneniya v banakhovom prostranstve”, Diff. uravn., 34:6 (1998), 841–843 | MR | Zbl

[25] Tikhonov I. V., “Soobrazheniya monotonnosti v obratnoi zadache dlya abstraktnogo differentsialnogo uravneniya”, Integralnye preobr. i spets. f-tsii. Inform. byulleten, 2:1 (2001), 119–128 | MR

[26] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967 | MR

[27] Sedletskii A. M., “O polnote sistemy eksponent v prostranstvakh differentsiruemykh funktsii”, Voprosy teorii signalov v radiotekhnicheskikh sistemakh, Tematicheskii sb., Tr. MEI, 334, M., 1977, 98–103