MD132 Pololineární diferenciální rovnice

Faculty of Science
Spring 2007
Extent and Intensity
2/0. 2 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 07011
Prerequisites
Finished the couse M 5160 ``Differential Equations and Continous Models
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The aim of the course is to present basic methods and results of the qualitative theory of half-linear differential equations. The main attention will be devoted to oscillation and asymtotic theory and to the theory of boundary value problems. Comparison of the half-linear methods and results with linear ones will be presented as well.
Syllabus
  • 1. Základy kvalitativní teorie pololineárních rovnic. 1.1. Existence a jednoznačnost; 1.2. Sturmovaská teorie; 1.3. Některé elementární pololineární rovnice. 2.Oscilační a asymptotická teorie: 2.1. Oscilační a neoscilační kriteria; 2.2. Asymptotika neoscilačních řešení; 2.3. Hlavní řešení pololineárních rovnic; 2.4. Konjugovanost a diskonjugovanost. 3.Okrajové úlohy 3.1. Úloha Sturmova-Liouvilleova typu pro pololineární rovnice; 3.2. Fredholmova alternativa, okrajové úlohy v rezonanci; 3.3. Parciální diferenciální rovnice s p-Laplaciánem; 3.4. Pololineární diferenční rovnice.
Literature
  • DOŠLÝ, Ondřej and Pavel ŘEHÁK. Half-Linear Differential Equations (Half-Linear Differrential Equations). Amsterdam: Elsevier, 2005, 517 pp. North-Holland Mathematics Studies. ISBN 0-444-52039-2. info
  • DOŠLÝ, Ondřej. Half-Linear Differential Equations. In Handbook of Differential Equations: Ordinary Differential Equations, I. Amsterdam: Elsevier, 2004, p. 161-357. Handbooks in Mathematics. ISBN 0-444-51128-8. info
Assessment methods (in Czech)
Ústní zkouška
Language of instruction
Czech
Further Comments
The course is taught only once.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2007/MD132