Menu: Home :: go to Journal :: switch to Russian :: switch to English
You are here: all Journals and Issues→ Journal→ Issue→ Article

THE CONDITIONS OF THE COVERING PROPE- RTY FOR THE NEMYTSKIY OPERATOR IN LEBEGUES SPACES

Annotation

We consider the superposition operator (the Nemytskiy operator) acting in the spaces of integrable functions. It is assumed that a function f(t, x) generating this operator satisfies the Caratheodory conditions and is α -covering with respect to the second argument on the family of centers and radii «of the covering balls» A(t) ⊂ Rn × R+. Knowing α and A(t), for the Nemytskiy operator, we get the constant of covering and find a family of centers and radii of the balls in the space of integrable functions.

Keywords

covering mappings of metric spaces; the Nemytskiy operator in spaces of integrable functions

Full-text in one file

Download

UDC

517.988.5

Pages

992-995

References

1. Avakov E.R., Arutyunov A.V., Zhukovskiy E.S. Nakryvayushchie otobrazheniya i ikh prilozheniya k differentsial'nym uravneniyam, ne razreshennym otnositel'no proizvodnoy // Differentsial'nye uravneniya. 2009. T. 45. № 5. S. 613–634. 2. Arutyunov A.V., Zhukovskiy E.S., Zhukovskiy S.E. O korrektnosti differentsial'nykh uravneniy, ne razreshennykh otnositel'no proizvodnoy // Differentsial'nye uravneniya. 2011. T. 47. № 11. S. 1523–1537. 3. Arutyunov A.V., Zhukovskii E.S, Zhukovskii S.E. Covering mappings and well-posedness of nonlinear Volterra equations // Nonlinear Analysis: Theory, Methods and Applications. 2012. V. 75. P. 1026–1044. 4. Zhukovskiy E.S., Pluzhnikova E.A. Nakryvayushchie otobrazheniya v probleme korrektnosti kraevykh zadach dlya differentsial'nykh uravneniy, ne razreshennykh otnositel'no proizvodnoy // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2011. T. 16. № 4. S. 1082-1085. 5. Zhukovskiy E.S., Pluzhnikova E.A. Nakryvayushchie otobrazheniya v proizvedenii metricheskikh prostranstv i kraevye zadachi dlya differentsial'nykh uravneniy, ne razreshennykh otnositel'no proizvodnoy // Differentsial'nye uravneniya. 2013. T. 49. № 4. S. 439–455. 6.Zhukovskiy E.S., Pluzhnikova E.A. Ob upravlenii ob"ektami, dvizhenie kotorykh opisyvaetsya neyavnymi nelineynymi differentsial'nymi uravneniyami // Avtomatika i telemekhanika. 2015. № 1. S. 31–56. 7. Arutyunov A., Avakov E., Gel’man B., Dmitruk A., Obukhovskii V. Locally covering maps in metric spaces and coincidence points // J. Fixed Points Theory and Applications. 2009. V. 5. № 1. S. 105-127. 8. Mordukhovich B.S. Variational Analysis and Generalized Differentiation. Springer, 2005. V. 1. 9. Zhukovskiy S.E. Sravnenie razlichnykh opredeleniy nakryvayushchikh otobrazheniy // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2014. T. 19. № 2. S. 376–379. 10. Zhukovskiy S. On Covering Properties in Variational Analysis and Optimization // Set-Valued and Variational Analysis, 2015. DOI: 10.1007/s11228-014-0314-3. 11. Zabreyko P.P., Koshelev A.I., Krasnosel'skiy M.A., Mikhlin S.G., Rakovshchik L.S., Stetsenko V.Ya. Integral'nye uravneniya. SMB. M.: Nauka, 1968. 448 s. 12. Borisovich Yu.G., Gel'man B.D., Myshkis A.D., Obukhovskiy V.V. Vvedenie v teoriyu mnogoznachnykh otobrazheniy i differentsial'nykh vklyucheniy. M.: Fizmatlit, 2007. 224 s. 13. Varga Dzh. Optimal'noe upravlenie differentsial'nymi i funktsional'nymi uravneniyami. M., 1977. 624 s.

Received

2015-06-02

Section of issue

Scientific articles

Для корректной работы сайта используйте один из современных браузеров. Например, Firefox 55, Chrome 60 или более новые.