Geodesic
On measure-compact operators
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 44-51 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain new sufficient solvability conditions for equations with measure-compact operators congruous with partially additive ones. We also prove new conditions under which these operators belong to the class of locally condensing maps with respect to the Hausdorff measure of non-compactness. As an application of the results we prove one property of bifurcation points which occur, in particular, in nonlinear mechanics.
Keywords: regular spaces, partially additive operators, measure of non-equipotential absolute continuity, condensing maps, Hausdorff measure of non-compactness, Uryson operator, Hammerstein operator, Lorentz spaces, Orlicz spaces
Mots-clés : Lebesgue spaces. 
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     author = {N. A. Erzakova},
     title = {On measure-compact operators},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {44--51},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_9_a4/}
}
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N. A. Erzakova. On measure-compact operators. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 44-51. http://geodesic.mathdoc.fr/item/IVM_2011_9_a4/

[1] Birman M. Sh., Vilenkin N. Ya., Gorin E. A. i dr., Funktsionalnyi analiz, Ser. Spravochnaya matematicheskaya biblioteka, Nauka, M., 1972

[2] Akhmerov R. R., Kamenskii M. I., Potapov A. S. i dr., Mery nekompaktnosti i uplotnyayuschie operatory, Nauka, Novosibirsk, 1986 | Zbl

[3] Yerzakova N. A., “On measures of non-compactness in regular spaces”, Z. Anal. Anwend., 15:2 (1996), 299–307 | MR | Zbl

[4] Erzakova N. A., “Kompaktnost po mere i mera nekompaktnosti”, Sib. matem. zhurn., 38:5 (1997), 1071–1073 | MR | Zbl

[5] Erzakova N. A., “O nelineinykh operatorakh”, Nauchn. vestn. Moskovsk. gos. tekhn. un-ta grazhdanskoi aviatsii. Ser. matem. i fizika, 2009, no. 140, 57–64

[6] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I. i dr., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966

[7] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, Gostekhizdat, M., 1956

[8] Vainberg M. M., Variatsionnye metody issledovaniya nelineinykh operatorov, Fizmatgiz, M., 1956

[9] Erzakova N. A., “O razreshimosti uravnenii s chastichno additivnymi operatorami”, Funkts. analiz i ego prilozh., 44:3 (2010), 69–72 | MR