%0 Journal Article %T Multivalent guiding functions in the bifurcation problem of differential inclusions %A Kornev, Sergey %A Liou, Yeong-Cheng %J Journal of Nonlinear Sciences and Applications %D 2016 %V 9 %N 8 %@ ISSN 2008-1901 %F Kornev2016 %X In this paper we use the multivalent guiding functions method to study the bifurcation problem for differential inclusions with convex-valued right-hand part satisfying the upper Carathéodory and the sublinear growth conditions. %9 journal article %R 10.22436/jnsa.009.08.12 %U http://dx.doi.org/10.22436/jnsa.009.08.12 %P 5259--5270 %0 Book %T Vvedenie v teoriyu razmernosti: Vvedenie v teoriyu topologicheskikh prostranstv i obshchuyu teoriyu razmernosti %A P. S. Aleksandrov %A B. A. Pasynkov %D 1973 %I (Russian), [Introduction to dimension theory: An introduction to the theory of topological spaces and the general theory of dimension], Izdat. ''Nauka'' %C Moscow %F Aleksandrov1973 %0 Book %T Introduction to the theory of multivalued maps and differential inclusions, (Russian) 2nd Ed. %A Y. G. Borisovich %A B. D. Gel'man %A A. D. Myshkis %A V. V. Obukhovskiĭ %D 2011 %I Librokom %C Moscow %F Borisovich2011 %0 Book %T Multivalued differential equations, de Gruyter Series in Nonlinear Analysis and Applications %A K. Deimling %D 1992 %I Walter de Gruyter and Co. %C Berlin %F Deimling 1992 %0 Book %T Fixed point theory for decomposable sets %A A. Fryszkowski %D 2004 %I Topological Fixed Point Theory and Its Applications, Kluwer Academic Publishers %C Dordrecht %F Fryszkowski2004 %0 Book %T Topological fixed point theory of multivalued mappings %A L. Górniewicz %D 2000 %I Second edition, Topological Fixed Point Theory and Its Applications, Springer %C Dordrecht %F Górniewicz 2000 %0 Book %T Condensing multivalued maps and semilinear differential inclusions in Banach spaces %A M. Kamenskii %A V. V. Obukhovskiĭ %A P. Zecca %D 2001 %I De Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter and Co. %C Berlin %F Kamenskii2001 %0 Journal Article %T On the method of multivalent guiding functions for periodic solution of differential inclusions %A S. V. Kornev %J Autom. Remote Control %D 2003 %V 64 %F Kornev2003 %0 Journal Article %T Nonsmooth integral directing functions in the problems of forced oscillations %A S. V. Kornev %J Translation of Avtomat. i Telemekh, (2015), 31-43, Autom. Remote Control %D 2015 %V 76 %F Kornev2015 %0 Journal Article %T The method of generalized integral guiding function in the periodic problem of differential inclusions %A S. V. Kornev %J (Russian) The Bulletin of Irkutsk State University. Mathematics %D 2015 %V 13 %F Kornev2015 %0 Journal Article %T Multivalent guiding function in a problem on existence of periodic solutions of some classes of differential inclusions %A S. V. Kornev %J Izv. Vyssh. Uchebn. Zaved. Mat. %D 2016 %V 11 %F Kornev 2016 %0 Journal Article %T On asymptotics of solutions for differential inclusions with nonconvex right-hand side %A S. V. Kornev %J (Russian) The Bulletin of Voronezh State University. Phisics. Mathematics %D 2016 %V 1 %F Kornev 2016 %0 Journal Article %T On nonsmooth multivalent guiding functions %A S. V. Kornev %A V. V. Obukhovskiĭ %J (Russian) Differ. Uravn., 39 (2003), 1497-1502, translation in Differ. Equ. %D 2003 %V 39 %F Kornev2003 %0 Journal Article %T On some developments of the method of integral guiding functions %A S. V. Kornev %A V. V. Obukhovskiĭ %J Funct. Differ. Equ. %D 2005 %V 12 %F Kornev2005 %0 Journal Article %T Asymptotic behavior of solutions of differential inclusions and the method of guiding functions %A S. V. Kornev %A V. V. Obukhovskiĭ %J Translation of Differ. Uravn., 51 (2015), 700-705, Differ. Equ. %D 2015 %V 51 %F Kornev2015 %0 Journal Article %T On asymptotics of solutions for a class of functional differential inclusions %A S. V. Kornev %A V. V. Obukhovskiĭ %A J.-C. Yao %J Discuss. Math. Differ. Incl. Control Optim. %D 2014 %V 34 %F Kornev2014 %0 Journal Article %T Guiding functions and periodic solutions for inclusions with causal multioperators %A S. V. Kornev %A V. V. Obukhovskiĭ %A P. Zecca %J Appl. Anal. %D 2016 %V 2016 %F Kornev2016 %0 Book %T The operator of translation along the trajectories of differential equations %A M. A. Krasnosel'skiĭ %D 1968 %I Translations of Mathematical Monographs, Translated from the Russian by Scripta Technica, American Mathematical Society %C Providence, R.I. %F Krasnosel'skiĭ 1968 %0 Journal Article %T On a certain principle of existence of bounded, periodic and almost periodic solutions of systems of ordinary differential equations %A M. A. Krasnosel'skiĭ %A A. I. Perov %J (Russian) Dokl. Akad. Nauk SSSR %D 1958 %V 123 %F Krasnosel'skiĭ1958 %0 Book %T Geometrical methods of nonlinear analysis %A M. A. Krasnosel'skiĭ %A P. P. Zabreĭko %D 1984 %I Translated from the Russian by Christian C. Fenske, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag %C Berlin %F Krasnosel'skiĭ1984 %0 Book %T Homotopy Properties of Set-Valued in Mappings %A W. Kryszewski %D 1997 %I University Nicholas Copernicus Publishing %C Toruń %F Kryszewski1997 %0 Journal Article %T Existence and global bifurcation of periodic solutions to a class of differential variational inequalities %A Z. Liu %A N. V. Loi %A V. V. Obukhovskiĭ %J Internat. J. Bifur. Chaos Appl. Sci. Engrg. %D 2013 %V 23 %F Liu2013 %0 Journal Article %T On an A-bifurcation theorem with application to a parameterized integro- differential system %A N. V. Loi %A Z. Liu %A V. V. Obukhovskiĭ %J Fixed Point Theory %D 2015 %V 16 %F Loi2015 %0 Journal Article %T A bifurcation of solutions of nonlinear Fredholm inclusions involving CJ-multimaps with applications to feedback control systems %A N. V. Loi %A V. V. Obukhovskiĭ %A J.-C. Yao %J Set-Valued Var. Anal. %D 2013 %V 21 %F Loi2013 %0 Journal Article %T A multiparameter global bifurcation theorem with application to a feedback control system %A N. V. Loi %A V. V. Obukhovskiĭ %A J.-C. Yao %J Fixed Point Theory %D 2015 %V 16 %F Loi2015 %0 Book %T On asymptotics of solutions for some classes of differential inclusions via the generalized guiding functions method %A V. V. Obukhovskiĭ %A M. Kamenskiĭ %A S. V. Kornev %A Y.-C. Liou %D 2016 %I submitted to J. Nonlin. Conv. Anal. %C %F Obukhovskiĭ2016 %0 Journal Article %T Existence and global bifurcation of solutions for a class of operator- differential inclusions %A V. V. Obukhovskiĭ %A N. V. Loi %A S. V. Kornev %J Differ. Equ. Dyn. Syst. %D 2012 %V 20 %F Obukhovskiĭ2012 %0 Book %T Method of guiding functions in problems of nonlinear analysis %A V. V. Obukhovskiĭ %A P. Zecca %A N. V. Loi %A S. V. Kornev %D 2013 %I Lecture Notes in Mathematics, Springer %C Heidelberg %F Obukhovskiĭ2013 %0 Journal Article %T Multivalent guiding functions in forced oscillation problems %A D. I. Rachinskiĭ %J Nonlinear Anal. %D 1996 %V 26 %F Rachinskiĭ1996