. . " semipositon problems" . " equations with degenerated and singular coefficients" . " variational arguments" . . " nonlinear eigenvalue problems" . " singular nonlinearities" . "2013-02-01+01:00"^^ . "V tomto projektu se budeme zab\u00FDvat r\u016Fzn\u00FDmi typy semiline\u00E1rn\u00EDch a kvaziline\u00E1rn\u00EDch diferenci\u00E1ln\u00EDch rovnic a jejich soustav. Pomoc\u00ED topologick\u00FDch a varia\u010Dn\u00EDch metod dok\u00E1\u017Eeme v\u011Bty o existenci a n\u00E1sobnosti \u0159e\u0161en\u00ED, pop\u0159\u00EDpad\u011B jejich bifurkac\u00ED. Numerick\u00E1 anal\u00FDza bude slou\u017Eit jako n\u00E1stroj dvou rozd\u00EDln\u00FDch koncept\u016F: bu\u010F jako motivace a ilustrace na\u0161ich teoretick\u00FDch v\u00FDsledk\u016F, anebo v souvislosti s u\u017Eit\u00EDm intervalov\u00E9 aritmetiky jako sou\u010D\u00E1st rigor\u00F3zn\u00EDch d\u016Fkaz\u016F. Zam\u011B\u0159\u00EDme se na otev\u0159en\u00E9 probl\u00E9my pro stacion\u00E1rn\u00ED a evolu\u010Dn\u00ED rovnice. Speci\u00E1ln\u00ED pozornost bude v\u011Bnov\u00E1na semiline\u00E1rn\u00EDm rovnic\u00EDm se sk\u00E1kaj\u00EDc\u00EDmi nelinearitami, kvaziline\u00E1rn\u00EDm rovnic\u00EDm obsahuj\u00EDc\u00EDm tzv. p-laplaci\u00E1n, co se t\u00FDk\u00E1 stacion\u00E1rn\u00EDch rovnic, a Fischerov\u011B-Kolmogorov\u011B rovnici a jej\u00EDm r\u016Fzn\u00FDm (kvaziline\u00E1rn\u00EDm) zobecn\u011Bn\u00EDm, co se t\u00FDk\u00E1 evolu\u010Dn\u00EDch rovnic." . "0"^^ . "In this project we focus on different types of semilinear and quasilinear differential equations and systems. We apply topological and variational methods to prove the existence and multiplicity of solutions as well as bifurcations of solutions. Numerical analysis will be used in two different contexts: either to motivate and illustrate our theoretical results or else in connection with interval atithmetics as part of rigorous proofs. We focus on open problems for both stationary and evolutionary equations. Our special attention will be paid to semilinear problems with jumping nonlinearities, quasilinear equations of the p-Laplacian type as for the stationary problems, and to Fischer-Kolmogorov equation and its various (quasilinear) generalizations as for the evolutionary ones."@en . "0"^^ . . "1"^^ . . "http://www.isvav.cz/projectDetail.do?rowId=GA13-00863S"^^ . "2015-04-23+02:00"^^ . . . " p-Laplacian" . " subcritical growth" . . "jumping nonlinearities, Fu\u010D\u00EDk spectrum, p-Laplacian, nonlinear eigenvalue problems, semipositon problems, subcritical growth, singular nonlinearities, equations with degenerated and singular coefficients, topological degree, variational arguments, sub a\u2026"@en . " Fu\u010D\u00EDk spectrum" . . " topological degree" . "15"^^ . "GA13-00863S" . "Semiline\u00E1rn\u00ED a kvaziline\u00E1rn\u00ED diferenci\u00E1ln\u00ED rovnice: existence a n\u00E1sobnost \u0159e\u0161en\u00ED" . "15"^^ . . . "2017-12-31+01:00"^^ . . . . . "jumping nonlinearities" . . "2014-04-18+02:00"^^ . . "Semilinear and Quasilinear Differential Equations: Existence and Multiplicity Results"@en .