. " quadratic functional" . "1"^^ . . . " symplectic and Hamiltonian system" . . . "2011-06-14+02:00"^^ . " asymptotic and oscillatory properties" . . . "Asymptotika, oscilace a kvadratick\u00E9 funkcion\u00E1ly v teorii dynamick\u00FDch rovnic" . . . "This project is focused on the study of asymptotic and oscillatory properties of linear, half-linear, and nonlinear equations, symplectic and Hamiltonian systems, and associated quadratic functionals. The results will be connected with optimality conditions for nonlinear problems in the calculus of variations and optimal control, since the second variation of these problems is a quadratic functional. An important aspect of this project is the inclusion of the theory of dynamic equations on time scales, which allows to study differential and difference equations and systems within one theory, to explain and understand the discrepancies between these theories, and at the same time to generalize them to other time scales. We will focus e.g. on symplectic systems without normality or on the theory of conjugate and coupled points for these systems. Furthermore, we will study effective criteria for the existence of solutions with prescribed properties and open problems arising in this area."@en . . "KJB100190701" . "33"^^ . "33"^^ . . "Asymptotics, oscillation, and quadratic functionals in theory of dynamic equations"@en . "2009-04-28+02:00"^^ . "During this project we solved all crucial problems listed in the grant application. Except of these particular topics, the we studied other research topics, which are closely related to the projects described in the application. We have 29 publications."@en . "2007-01-01+01:00"^^ . . . . . "B\u011Bhem doby trv\u00E1n\u00ED projektu se poda\u0159ilo vy\u0159e\u0161it t\u00E9m\u011B\u0159 v\u0161echny z\u00E1sadn\u00ED probl\u00E9my uveden\u00E9 v\u00A0grantov\u00E9 p\u0159ihl\u00E1\u0161ce. Krom\u011B t\u011Bchto t\u00E9mat se \u0159e\u0161itel\u00E9 zab\u00FDvali dal\u0161\u00EDmi v\u00FDzkumn\u00FDmi projekty, kter\u00E9 navazuj\u00ED na problematiku popsanou v n\u00E1vrhu. V\u00FDsledkem je 29 publikac\u00ED."@cs . . "Projekt je zam\u011B\u0159en na studium asymptotick\u00FDch a oscila\u010Dn\u00EDch vlastnost\u00ED line\u00E1rn\u00EDch, pololine\u00E1rn\u00EDch a neline\u00E1rn\u00EDch rovnic, symplektick\u00FDch a Hamiltonovsk\u00FDch syst\u00E9m\u016F a k nim p\u0159\u00EDslu\u0161ej\u00EDc\u00EDch kvadratick\u00FDch funkcion\u00E1l\u016F. V\u00FDsledky budou d\u00E1v\u00E1ny do souvislosti s podm\u00EDnkami optimality pro neline\u00E1rn\u00ED \u00FAlohy varia\u010Dn\u00EDho po\u010Dtu a optim\u00E1ln\u00EDho \u0159\u00EDzen\u00ED, nebo\u0165 druh\u00E1 variace takov\u00FDch probl\u00E9m\u016F je kvadratick\u00FDm funkcion\u00E1lem. Jedn\u00EDm z d\u016Fle\u017Eit\u00FDch aspekt\u016F projektu je za\u010Dlen\u011Bn\u00ED teorie dynamick\u00FDch rovnic na %22time scales%22, co\u017E umo\u017E\u0148uje studovat diferenci\u00E1ln\u00ED a diferen\u010Dn\u00ED rovnice a syst\u00E9my v r\u00E1mci jedin\u00E9 teorie, zd\u016Fvodnit a pochopit rozd\u00EDly mezi t\u011Bmito teoriemi a z\u00E1rove\u0148 zobecnit tyto teorie na mnoh\u00E9 jin\u00E9 time scales. Zam\u011B\u0159\u00EDme se nap\u0159\u00EDklad na studium symplektick\u00FDch syst\u00E9m\u016F bez p\u0159edpokladu normality \u010Di na teorii konjugovan\u00FDch a sdru\u017Een\u00FDch bod\u016F pro tyto syst\u00E9my. D\u00E1le budeme studovat efektivn\u00ED podm\u00EDnky pro existenci \u0159e\u0161en\u00ED s p\u0159edepsan\u00FDmi vlastnostmi a otev\u0159en\u00E9 probl\u00E9my, kter\u00E9 se objevily p\u0159i studiu popisovan\u00FDch objekt\u016F." . " and dynamic equation" . "Differential" . . " time scale" . " difference" . "2"^^ . "2009-12-31+01:00"^^ . . "0"^^ . "http://www.isvav.cz/projectDetail.do?rowId=KJB100190701"^^ . "Differential, difference, and dynamic equation; quadratic functional; asymptotic and oscillatory properties; second order optimality conditions; time scale; symplectic and Hamiltonian system; half/quasi-linear equation"@en . " second order optimality conditions" .