Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MME0010	Special Topics in Differential Equations	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Romanian	5	2+1+0	speciality	optional	
Mathematics-Computer Science - in Romanian	5	2+1+0	speciality	optional	
Applied Mathematics	5	2+1+0	speciality	optional	

Teaching Staff in Charge	Prof. PRECUP Radu, Ph.D., r.precup@math.ubbcluj.ro
Lect. 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	
Bibliography	1. R.P. Agarwal, D. O&#8217;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