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ABOUT OPERATOR EQUATIONS WITH SURJECTIVE QUASI INVERTIBLE OPERATORS

Annotation

This article examines operator equation with a linear surjective operator A which can be not closed, but has a continuous right inverse mapping. The existence theorem for the solutions set of the operator equation A(x) = f(x), where A is a surjective linear operator, and f is a completely continuous mapping, is proven; the applications of the theorem are considered.

Keywords

quasi invertible operator; surjective operator; topological degree; operator equation

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UDC

517.988.6

Pages

1120-1122

References

1. Gel'man B.D., Rydanova S.S. Ob operatornykh uravneniyakh s syur"ektivnymi operatorami // Vestnik Voronezhskogo Gosudarstvennogo Universiteta. Seriya: Fizika. Matematika. Voronezh, 2012. № 1. S. 93-98. 2. Rydanova S.S. Ob odnom klasse operatornykh uravneniy // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2011. T. 16. Vyp. 4. S. 1173-1174. 3. Gubina S.S. Teorema Borsuka-Ulama dlya kvaziobratimykh operatorov. Nekotorye prilozheniya // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2013. T. 18. Vyp. 5. S. 2496-2498. 4. Krasnosel'skiy M.A., Zabreyko P.P. Geometricheskie metody nelineynogo analiza. M., 1975. 5. Gel'man B.D. Topologicheskie svoystva mnozhestva nepodvizhnykh tochek mnogoznachnykh otobrazheniy // Matematicheskiy sbornik. 1997. T. 188. № 12. S. 33-56.

Received

2015-06-09

Section of issue

Scientific articles

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