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Recommended for master students of mathematical analysis.
Content: Mountain pass lemma, topological degree, Leray-Schauder degree, monotone operatorsin a Hilbert
space, nonlinear semigroups, bifurcations.
Last update: Pyrih Pavel, doc. RNDr., CSc. (09.06.2021)
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Zápočet bude udělován za nadpoloviční účast na cvičeních. Kvůli koronaviru zápočet dostanou automaticky všichni. Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu. Last update: Hencl Stanislav, prof. RNDr., Ph.D. (24.04.2020)
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P. Drábek, J. Milota: Methods of nonlinear analysis. Applications to differential equations. Birkhäuser Verlag, Basel, 2007. L. C. Evans: Partial differential equations. AMS, Providence, RI, 2010 Last update: T_KMA (02.05.2013)
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Zkouška je ústní, lze ji vykonat i distančně například po Skypu. Požadavky ke zkoušce odpovídají sylabu předmětu v rozsahu, jak byl probrán. Last update: Hencl Stanislav, prof. RNDr., Ph.D. (24.04.2020)
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1. Weak convergence in L_1 characterization, biting lemma 2. Problems convex in the last variable 3. Generalized convexity (briefly) rank-1 convexity, polyconvexity, kvaziconvexity 4. Mountain pass lemma Ekeland variational principle, Palais-Smale condition 5. Nonlinear semigroup 6. Bifurcation Crandall-Rabinowitz theorem, bifurcation from the point of spectrum with odd multiplicity, variational problem and bifurcation from the point of a spectrum with even multiplicity Last update: Kaplický Petr, doc. Mgr., Ph.D. (09.06.2015)
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Elements of linear functional analysis, elements of measure theory, theory of Lebesgue integral, function spaces. Last update: Spurný Jiří, prof. RNDr., Ph.D., DSc. (10.05.2018)
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