Multiplicity results for two kinds of equivariant systems Original Research Article

Two equivariant problems of the form εΔu=∇F(u)εΔu=∇Fu are considered, where FF is a real function which is invariant under the action of a group GG, and, using Morse theory, for each problem an arbitrarily great number of orbits of solutions is founded, choosing εε suitably small. The first problem is a O(2)O2-equivariant system of two equations, which can be seen as a complex Ginzburg-Landau equation, while the second one is a system of mm equations which is equivariant for the action of a finite group of real orthogonal matrices m×mm×m.