The effect of the domain topology on the number of positive solutions of an elliptic system involving critical Sobolev exponents. (English) Zbl 1200.35116
Summary: We consider the Dirichlet problem for an elliptic system of two equations involving the critical Sobolev exponents. We first establish the concentration-compactness principle for elliptic systems; then by the variational method and applying Lyusternik-Schnirelmann theory, we study the effect of the domain topology on the number of positive solutions.
MSC:
35J60 | Nonlinear elliptic equations |
35J50 | Variational methods for elliptic systems |
35B33 | Critical exponents in context of PDEs |