"Topological and variational methods for nonlinear boundary value problems"@en . . . . . . . . "Jedn\u00E1 se o velice kvalitn\u00ED projekt s velk\u00FDm p\u0159\u00EDnosem pro dan\u00FD obor. Bylo dosa\u017Eeno nejen nov\u00FDch matematick\u00FDch v\u00FDsledk\u016F, ale zavedeny i nov\u00E9 metody pro vy\u0161et\u0159ov\u00E1n\u00ED zkouman\u00FDch typ\u016F rovnic. Velk\u00FD v\u00FDznam m\u00E1 i projektem potvrzen\u00E1 spolupr\u00E1ce odborn\u00EDk\u016F se studen"@cs . . "http://www.isvav.cz/projectDetail.do?rowId=GA201/97/0395"^^ . . . "Projekt je sou\u010D\u00E1st\u00ED \u0161ir\u0161\u00ED problematiky \u0159e\u0161en\u00E9 na kated\u0159e matematiky Fakulty aplikovan\u00FDch v\u011Bd Z\u00E1pado\u010Desk\u00E9 univerzity v Plzni. Technick\u00E9 z\u00E1zem\u00ED poskytne ned\u00E1vno otev\u0159en\u00E9 superpo\u010D\u00EDta\u010Dov\u00E9 centrum na Z\u010CU v Plzni. C\u00EDlem je kvalitativn\u00ED studium spojit\u00FDch matematick\u00FDch model\u016F, formulovan\u00FDch jako okrajov\u00E9 \u00FAlohy pro oby\u010Dejn\u00E9 a parci\u00E1ln\u00ED diferenci\u00E1ln\u00ED rovnice. Budou rozv\u00EDjeny nov\u00E9 varia\u010Dn\u00ED metody zalo\u017Een\u00E9 na my\u0161lence prof. S.I.Pocho\u017Eajeva a aplikov\u00E1ny na neline\u00E1rn\u00ED \u00FAlohy obsahuj\u00EDc\u00ED nelinearitu typu p-Laplaci\u00E1n. Nateorii stupn\u011B zobrazen\u00ED je zalo\u017Een topologick\u00FD p\u0159\u00EDstup k ot\u00E1zk\u00E1m existence a stability \u0159e\u0161en\u00ED dynamick\u00FDch syst\u00E9m\u016F s jedn\u00EDm a v\u00EDce stupni vlonosti. Studium v\u00E1hov\u00FDch prostor\u016F a Hardyovy nerovnosti je z\u00E1kladem vy\u0161et\u0159ov\u00E1n\u00ED neline\u00E1rn\u00EDch okrajov\u00FDch \u00FAloh pro d egenerovan\u00E9 a singul\u00E1rn\u00ED rovnice a spektr\u00E1ln\u00ED anal\u00FDzy degenerovan\u00FDch a singul\u00E1rn\u00EDch diferenci\u00E1ln\u00EDch oper\u00E1tor\u016F. V\u00FDsledky budou publikov\u00E1ny v mezin\u00E1rodn\u00EDch \u010Dasopisech." . . "This project is a part of problematics solved at the Department of Mathematics of the Faculty of Applied Sciences of the University of West Bohemia (UWB) in Pilsen. Supercomputer center opened recently at UWB in Pilsen will provide necessary technical support. The main goal is a qualitative study of continuous mathematical models formulated as a boundary value problems for ODEs and PDEs. We will investigate new variational methods due to prof. S.I. Pohozaev and to aply them to nonlinearities of the typeof p-Laplacian. Degree theory is a starting point of the topological approach to the existence and stability theory for dynamical systems with one and more degrees of freedom. The study of weighted spaces and Hardy's inequality is abackgroundfor the inv estigation of nonlinear boundary value problems for degenerated and singular equations and spectral analysis of degenerated and singular differential operators. The results will be published in international journals."@en . "0"^^ . . "Topologick\u00E9 a varia\u010Dn\u00ED metody \u0159e\u0161en\u00ED neline\u00E1rn\u00EDch okrajov\u00FDch \u00FAloh" . "33"^^ . "GA201/97/0395" . . . "33"^^ . "0"^^ . "1"^^ .