On bifurcation points of strongly condensing operators
Abstract
Two conditions equivalent to complete continuity of Frechet derivative at a point and the asymptotic derivative in the case of their existence are given. Theorem of M.A. Krasnosel’skii on asymptotic bifurcation points for completely con-tinuous fields to class of strongly - condensing at infinity vector fields is generalized.
References
1. Akhmerov R.R., Kamenskii M.I., Potapov A.S., Rodkina A.E., Sadovskii B.N. Measures of Noncompactness and Condensing Operators. B irkhaser Verlag, Basel, Boston, Berlin, 1992.
2. Erzakova N.A. On locally condensing operators // Nonlinear Analysis: Theory Methods& Applications, 2012, vol. 75, no. 8, pp. 3552-3557.
3. Erzakova N. A. Nauchnyi vestnik MGTU GA, 2014, no. 207, pp.110-117.
4. Krasnosel'skii, M. A. Topological Methods in the Theory of Nonlinear Integral Equations, A Pergamon Press Book The Macmillan Co., New York, 1964.
5. Melamed, V.B., Perov, A.I. A generalization of a theorem of M.A. Krasnosel'skii on the complete continuity of the Frechet derivative of a completely continuous operator // Sibirskij matematiceskij zurnal, 1963, no. 4.3, pp. 702-704.
6. Erzakova N. A. On a criterion for the complete continuity of the Frechet derivative // Functional Analysis and its Applications (in print).
7. Erzakova N.A. Generalization of some M.A. Krasnosel'skii's results // Journal of Mathematical Analysis and Applications, 2015, DOI information:10.1016/j.jmaa.2015.03.063.
8. Krasnosel'skii M. A.; Zabreiko P.P. Geometric Methods of Nonlinear Analysis, Grundlehrer der mathematischen Wissenschaften Vol. 263, Springer-Verlag, Berlin, New York, 1984.
9. Erzakova N.A. On Measure-Compact Operators / Russian Mathematics (Iz. VUZ.), 2011, vol. 55, no. 9. pp. 37-45.
Review
For citations:
Erzakova N.A. On bifurcation points of strongly condensing operators. Civil Aviation High Technologies. 2015;(220):105-113. (In Russ.)
Views:
367
Email this article 
