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the radially symmetric solution w(x) = (w + , w − ) : R 2 → C 2 of degree pair (1, 1) was given by A. Alama and Q. Gao in J. Differential Equations 255 (2013), 3564-3591. We will concern its linearized operator L around w and prove the non-degeneracy result under one more assumption B < 0: the kernel of L is spanned by the functions ∂w ∂x 1 and ∂w ∂x 2 in a natural Hilbert space. As an application of the non-degeneracy result, a solvability theory for the linearized operator L will be given.

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> 0, we will concern its linearized operator L around the radially symmetric solution w(x) = (w + , w − ) : R 2 → C 2 of degree pair (1, 1) and prove the non-degeneracy result: the kernel of L is spanned by ∂w ∂x 1 , ∂w ∂x 2 in a natural Hilbert space. As an application of the non-degeneracy result, a solvability theory for the linearized operator L will be given.

No abstract