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Nonlinear Functional Analysis 2 - NMMA502

Title:	Nelineární funkcionální analýza 2
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2025 to 2025
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time

Guarantor:	prof. RNDr. Stanislav Hencl, Ph.D.
Teacher(s):	prof. RNDr. Stanislav Hencl, Ph.D.
Class:	M Mgr. MA M Mgr. MA > Povinné
Classification:	Mathematics > Functional Analysis

Opinion survey results SS schedule Noticeboard

Annotation -

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)

Course completion requirements - Czech

Zápočet bude udělován za aktivní účast na cvičení - předvedení nějakého ze zadaných úkolů.

Last update: Hencl Stanislav, prof. RNDr., Ph.D. (09.02.2026)

Literature - Czech

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)

Requirements to the exam - Czech

Proběhne ústní zkouška, požadavky odpovídají sylabu v rozsahu, jak byl prezentován na přednášce.

Last update: Hencl Stanislav, prof. RNDr., Ph.D. (09.02.2026)

Syllabus -

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

Last update: Hencl Stanislav, prof. RNDr., Ph.D. (09.02.2026)

Entry requirements -

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)