Multiple solutions for semilinear elliptic systems involving critical Sobolev exponent. (English) Zbl 1212.35101

Summary: The effect of the domain topology on the multiplicity of solutions for a semilinear elliptic system with critical Sobolev exponent is discussed. We show that if the coupling term is sufficiently small, then there exist at least \(\operatorname {cat}\Omega \) positive solutions, where \(\operatorname {cat}\) denotes the Ljusternik-Schnirelman category.


35J50 Variational methods for elliptic systems
55M30 Lyusternik-Shnirel’man category of a space, topological complexity √† la Farber, topological robotics (topological aspects)