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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 2016 to 2016
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:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Jiří Spurný, Ph.D., DSc.
Class:	M Mgr. MA M Mgr. MA > Povinné
Classification:	Mathematics > Functional Analysis

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Annotation -

Last update: doc. RNDr. Pavel Pyrih, CSc. (09.06.2021)

Mandatory course of the master study branch Mathematical analysis. Recommended for the second year of master studies. Content: Mountain pass lemma, topological degree, Leray-Schauder degree, monotone operators in a Hilbert space, nonlinear semigroups, bifurcations.

Literature - Czech

Last update: T_KMA (02.05.2013)

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

Syllabus -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (09.06.2015)

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