Geodesic
On the question of extended convexity of Green operator
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 26-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $Q$ be a differential operator of order $m-1$, $2\leqslant m \leqslant n$, for which $(a, b)$ is the interval of nonoscillation, and the Green's operator $G\colon L[a, b]\to W^n[a, b]$ of boundary value problem $Lx=f$, $l_i(x)=0$, $i=1,\dots,n$ has the property of generalized convexity: $QGP>0$ for some linear homeomorphism $P$ of Lebesgue space $L[a,b]$. Under some conditions, we prove, that the perturbed boundary value problem $Lx=PVQx+f$, $l_i(x)=0$, $i=1,\dots,n$ is also uniquely solvable in the Sobolev space $W^n[a,b]$ and the Green's operator $\widehat G$ inherits the property of $G$, that is $Q\widehat GP>0$.
Keywords: Green's operator, extended convexity. 
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G. G. Islamov. On the question of extended convexity of Green operator. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 26-31. http://geodesic.mathdoc.fr/item/VUU_2012_1_a2/

[1] Azbelev N. V., Rakhmatullina L. F., Maksimov V. P., Metody sovremennoi teorii lineinykh funktsionalno-differentsialnykh uravnenii, NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2000, 300 pp.

[2] Islamov G. G., “Otsenki minimalnogo ranga konechnomernykh vozmuschenii operatorov Grina”, Differentsialnye uravneniya, 25:9 (1989), 1496–1503 | MR | Zbl

[3] Islamov G. G., “O nekotorykh prilozheniyakh teorii abstraktnogo funktsionalno-differentsialnogo uravneniya. I”, Differentsialnye uravneniya, 25:11 (1989), 1872–1881 | MR | Zbl

[4] Islamov G. G., “O nekotorykh prilozheniyakh teorii abstraktnogo funktsionalno-differentsialnogo uravneniya. II”, Differentsialnye uravneniya, 26:2 (1990), 224–232 | MR | Zbl

[5] Islamov G. G., “Kriterii razreshimosti uravnenii s kraevymi neravenstvami”, Izvestiya instituta matematiki i informatiki UdGU (Izhevsk), 1994, no. 2, 3–24 | Zbl

[6] Azbelev N. V., Rakhmatullina L. F., Tsalyuk Z. B., “Zametka o polozhitelnosti obratnykh operatorov”, Uchënye zapiski Udmurtskogo gospedinstituta, 1958, no. 12, 47–49

[7] Vulikh B. Z., Vvedenie v teoriyu poluuporyadochennykh prostranstv, Fizmatgiz, M., 1961, 408 pp. | MR | Zbl

[8] Islamov G. G., “O suschestvovanii polozhitelnykh reshenii uravnenii s zapazdyvayuschim argumentom”, Materialy tretei Vsesoyuz. mezhvuz. konf. po teorii i prilozheniyam differ. uravn. s otklonyayuschimsya argumentom, Chernovtsy, 1972, 95–97

[9] Karlin S., Stadden V., Chebyshevskie sistemy i ikh primenenie v analize i statistike, Nauka, M., 1976, 568 pp. | MR

[10] Islamov G. G., “K voprosu ob otsenke sverkhu spektralnogo radiusa”, Vestnik Udmurtskogo universiteta. Matematika, 1992, no. 1, 82–86 | MR | Zbl