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

Ishiwata, Michinori

Differ. Integral Equ. 20, No. 11, 1237-1252 (2007).

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.

MSC:

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

Keywords:

semilinear elliptic system; critical Sobolev exponent; multiplicity of solutions; Ljusternik-Schnirelman category