"Projekt je zam\u011B\u0159en k dal\u0161\u00EDmu rozvoji teorie sou\u010Dtov\u00E9 integrace a aplikac\u00EDm na zobecn\u011Bn\u00E9 oby\u010Dejn\u00E9 diferenci\u00E1ln\u00ED rovnice (ODR) a v d\u016Fsledku na r\u016Fzn\u00E9 typy klasick\u00FDch diferenci\u00E1ln\u00EDch rovnic. C\u00EDlem je pokra\u010Dovat ve studiu sou\u010Dtov\u00FDch integr\u00E1l\u016F Henstockova-Kurzweilova typu pro funkce s hodnotami v Banachov\u011B prostoru a nov\u011B vytvo\u0159it jednotnou teorii zobecn\u011Bn\u00FDch ODR, kter\u00E1 m\u00E1 zahrnout sou\u010Dasn\u011B p\u0159\u00EDpad rovnic s rychle osciluj\u00EDc\u00ED pravou stranou a ODR Carath\u00E9odoryova typu. V\u00FDznam projektu spo\u010D\u00EDv\u00E1 v rozvoji kvalitativn\u00ED teorii oby\u010Dejn\u00FDch a funkcion\u00E1ln\u00EDch diferenci\u00E1ln\u00EDch rovnic. O\u010Dek\u00E1v\u00E1me nov\u00E9 v\u00FDsledky v oblasti obecn\u00E9ho sou\u010Dtov\u00E9ho integr\u00E1lu a jej\u00EDch u\u017Eit\u00ED v teorii diferenci\u00E1ln\u00EDch a integr\u00E1ln\u00EDch rovnic. Na\u0161im c\u00EDlem je pokra\u010Dovat a z r\u016Fzn\u00FDch hledisek sjednotit dosud zn\u00E1m\u00E9 v\u00FDsledky. Pl\u00E1nujeme novou kni\u017En\u00ED publikaci v\u011Bnovanou zobecn\u011Bn\u00FDm ODR v Banachov\u011B prostoru." . "1"^^ . "2009-04-28+02:00"^^ . "2010-06-08+02:00"^^ . . . . . . "0"^^ . "http://www.isvav.cz/projectDetail.do?rowId=IAA100190702"^^ . "Byla ustanovena teorie zobecn\u011Bn\u00FDch diferenci\u00E1ln\u00EDch rovnic se zam\u011B\u0159en\u00EDm na rovnice,jejich\u017E \u0159e\u0161en\u00ED nemaj\u00ED kone\u010Dnou variaci. Byla vy\u0161et\u0159ena roz\u0161\u00ED\u0159en\u00ED pojm\u016F integr\u00E1l\u016F a dok\u00E1z\u00E1n vztah mezi zobecn\u011Bn\u00FDmi a funkcion\u00E1ln\u011B diferenci\u00E1ln\u00EDmi rovnicemi"@cs . . . "6"^^ . . . "Summation integration and generalized differential equations"@en . "6"^^ . "2007-01-01+01:00"^^ . "Kurzweil-Henstock integral" . . . . "IAA100190702" . . . "Theory of generalized differential equations was established with an attention to those whose solutions need not be of bounded variation. Extensions of known notions of integrals were considered and relationship between GODEs and FDEs was established"@en . . "Sou\u010Dtov\u00E1 integrace a zobecn\u011Bn\u00E9 diferenci\u00E1ln\u00ED rovnice" . "2009-12-31+01:00"^^ . "0"^^ . . . " generalized ordinary differential equations" . . "Kurzweil-Henstock integral; generalized ordinary differential equations; functional differential equations"@en . "The project is devoted to further development of the theory of the summation integration and its application to generalized ordinary differential equations (ODE) and consequently to various types of classical differential equations. Our aim is to continue the study of summation integrals of the Henstock-Kurzweil type of functions with values in a Banach space and to create a new unified theory of generalized ODE's which should cover both the cases of fastly oscillating right hand sides of an ODE and the case of an ODE of Carath\u00E9odory type. The signification of our project consists in the further development of the qualitative theory of ordinary and functional differential equations. We expect new results concerning the general summation integral and its applications in the theory of differential and integral equations. Our goal is to continue and to unify in many aspects the results obtained until now. We are planning a new book devoted to generalized ODE's in Banach spaces."@en .