Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT
| MME0010 | Special Topics in Differential Equations |
| Teaching Staff in Charge |
Prof. PRECUP Radu, Ph.D., r.precup math.ubbcluj.roLect. ANDRAS Szilard Karoly, andrasz math.ubbcluj.ro |
| Aims |
|
Advanced topics of ordinary differential equations; Theory of nonlinear differential equations. |
| Content |
|
1. Fredholm integral equations; existence and uniqueness
2. Volterra integral equations: Bielecki norms, existence and uniqueness 3. The Cauchy problem: existence in the space and ball 4. Upper and lower solution technique 5. The Green function 6. Autoadjoint equations 7. Nonlinear boundary value problems 8. Compact operators; application of Schauder@s fixed point theorem 9. The Leray-Schauder principle and applications 10 Stable solutions 11. Stability of linear systems 12. Stability of solutions of perturbed linear systems 13. The case of some systems from applied mathematrics |
| References |
|
1. R.P. Agarwal, D. O’Regan, An Introduction to Ordinary Differential Equations, Springer, 2008.
2. V. Barbu, Ecuatii diferentiale, Junimea, 1985. 3. R. Precup, Methods in Nonlinear Integral Equations, Kluwer, 2002. 4. L.C. Piccinini, G. Stampacchia, G. Vidossich, Ordinary Differential Equations in R^n, Springer, 1984. |
| Assessment |
|
20% activity to courses and seminaries
20% report 60% written exam |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |