| Capitole speciale de ecuaţii cu derivate parţiale |
trul |
|||||
| Cadre didactice indrumatoare |
| Prof. Dr. SZILAGYI Paul, szilagyp@cs.ubbcluj.ro |
| Obiective |
|
Asimilarea unor metode actuale din teoria ecuatiilor cu derivate partiale. |
| Continut |
|
Gradul topologic Browder si Leray-Schauder. Teoreme de punct fix. Operatori monotoni, maximal-monotoni, pseudo-monotoni. Teoreme de surjectie. Operatorul lui Nemâtchi. Spatii Sobolev, teoreme de scufundare. Probleme la limita pentru ecuatii eliptice si pentru sisteme eliptice neliniare. Probleme mixte pentru ecuatii parabolice neliniare. Inegalitati variationale. |
| Bibliografie |
|
1. Adams, R.A., Sobolev spaces. Academic Press, 1975.
2. Deimling, K., Nonlinear functional analysis. Springer, Berlin-Heidelberg-New-York-Tokyo, 1985. 3. Gilbarg, D., Trudinger, N.S., Elliptic partial differential equations of second order. Springer, Berlin, 1983. 4. Chebrowski, I., Variational methods for potential operator equations with applications to nonlinear elliptic equations. W. de Gruyter Studies in Mathematics. 24. Berlin, 1997. 5. Pascali, D., Sburlan, S., Nonlinear mappings of monotone type. Ed. Acad. And Sijthoff & Noorhoff, Bucuresti, Alphen, 1978. 6. Pascali, D., Topological methods in nonlinear analysis. Lecture notes in Mathematics, Univ. Constanta-New-York University, Courant Institute, 2001. 7. Precup, R., Ecuatii integrale neliniare. UBB Cluj, 1993. 8. Sburlan, S., Topological and functional methods for partial differential equations. Univ. Constanta, 1985. 9. Szilágyi P., Elliptic systems with discontinuous nonlinearity. Studia UBB, Math. XXXIX.4.1994, p. 11-20. |
| Evaluare |
|
Examen. |