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

Code	Subject	
MME1004	Topological Methods for Nonlinear Partial Differential Equations	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	3	2+2+0	speciality	optional	

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.
	
Bibliography	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