. . . . . . "A) Existen\u010Dn\u00ED princip pro periodick\u00E9 \u00FAlohy s Phi-Laplaci\u00E1nem zalo\u017Een\u00FD na existenci dvojice horn\u00EDch a doln\u00EDch funkc\u00ED byl roz\u0161\u00ED\u0159en na p\u0159\u00EDpad, \u017Ee tyto funkce nejsou uspo\u0159\u00E1dan\u00E9. Poda\u0159ilo se naj\u00EDt podm\u00EDnky zaru\u010Duj\u00EDc\u00ED, \u017Ee ka\u017Ed\u00E9 periodick\u00E9 \u0159e\u0161en\u00ED kvaziline\u00E1rn\u00ED"@cs . . "1"^^ . "Neuvedeno."@en . . . "Reimannian approach to integration in connection with classical mathematical analysis"@en . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/04/0690"^^ . "A) The existence principle for periodic problems with a Phi-Laplacian based on the existence of a couple of upper and lower functions was extended to the case when these functions are not ordered. Conditions have been found under which every periodic sol"@en . "0"^^ . "The aim of the project is to contribute to the general integration theory based on Riemannian sums with applications to differential equations, boundary value problems e.g. general non-linear boundary value problems for ordinary differential equations, singular evolution problems in the space of regulated functions with values in Hilbert and Banach spaces. Further to concentrate on the problem whether to an integrable function with respect to a given integration base there is a sequence of step-functions, which is convergent to f with respect to the corresponding convergence. Attention will be paid to summation integrals of the Henstock-Kurzweil and McShane type of functions with values in a Banach space and their comparison with the knownBochner, Pettis and Dunford integrations. New results concerning the theory of general summation integral even for Banach space-valued functions are expected which will deepen our knowledge in the field and in many aspects continue to unify the results"@en . "5"^^ . "2007-10-16+02:00"^^ . "5"^^ . . . . . . . . "C\u00EDlem projektu je p\u0159isp\u011Bt k obecn\u00E9 teorii integr\u00E1lu, kter\u00E1 je zalo\u017Eena na riemannovsk\u00FDch sou\u010Dtech, spolu s aplikacemi na diferenci\u00E1ln\u00ED rovnice, okrajov\u00E9 \u00FAlohy, nap\u0159. obecn\u00E9 neline\u00E1rn\u00ED okrajov\u00E9 \u00FAlohy pro oby\u010Dejn\u00E9 diferenci\u00E1ln\u00ED rovnice, singul\u00E1rn\u00ED evolu\u010Dn\u00EDprobl\u00E9my v prostoru regulovan\u00FDch funkc\u00ED s hodnotami v Hilbertov\u011B a Banachov\u011B prostoru. Pozornost bude v\u011Bnov\u00E1na probl\u00E9mu zda k funkci integrovateln\u00E9 vzhledem k jist\u00E9 integra\u010Dn\u00ED b\u00E1zi existuje posloupnost schodovit\u00FDch funkc\u00ED, kter\u00E1 k n\u00ED konverguje v konvergenci, ur\u010Den\u00E9 integra\u010Dn\u00ED b\u00E1z\u00ED. Rovn\u011B\u017E budou vy\u0161et\u0159ov\u00E1ny integr\u00E1ly Henstockova-Kurzweilova a McShaneova typu pro funkce s hodnotami v Banachov\u011B prostoru a budou porovn\u00E1ny se zn\u00E1m\u00FDmi integracemi Bochnerovou, Pettisovou a Dunfordovou. O\u010Dek\u00E1vaj\u00ED se nov\u00E9 v\u00FDsledky v teorii obecn\u00FDch sou\u010Dtov\u00FDch integr\u00E1l\u016F i pro funkce s hodnotami v Banachov\u00FDch prostorech, kter\u00E9 prohloub\u00ED znalosti v t\u00E9to oblasti a z r\u016Fzn\u00FDch hledisek pokro\u010D\u00ED ve sjednocov\u00E1n\u00ED dosud z\u00EDskan\u00FDch poznatk\u016F." . "Riemannovsk\u00FD p\u0159\u00EDstup k integraci v souvislosti s klasickou matematickou anal\u00FDzou" . . . "GA201/04/0690" . "0"^^ .