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