Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MME1004 | Topological Methods for Nonlinear Partial Differential Equations |
| Teaching Staff in Charge |
Prof. PRECUP Radu, Ph.D., r.precup math.ubbcluj.ro |
| Aims |
|
Fundamental methods for the study of nonlinear elliptic problems: homotopy methods; upper and lower solution method and critical point method. |
| Content |
|
1. Introduction: basic results from linear elliptic equations theory (maximum principle, eigenvalues and eigenfunctions, the Dirichlet principle, continuous and compact embedding theorems).
2. Homotopy methods: the Leray-Schauder continuation principle; $a priori$ bounds technique; applications. 3. Upper and lower solution technique. 4. Critical point method: variational formulation; the Ambrosetti-Rabinowitz mountain pass theorem; applications. |
| References |
|
1. R. Precup, Lectii de ecuatii cu derivate partiale, Presa Universitara Clujeana, Cluj, 2004.
2. R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht, 2002. 3. H. Brezis, Analyse fonctionnelle, Masson, Paris, 1983. 4. M. Struwe, Variational Methods, Springer, Berlin, 1990. 5. O. Kavian, Introduction a la Theorie des Points Critiques, Springer, Paris, 1995. |
| Assessment |
|
10% activity at courses and seminaries
40% scientific project 50% exam |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |