Bubbling solutions of mixed type for a general non-Abelian Chern–Simons–Higgs system of rank 2 over a torus

We consider a general non-Abelian Chern–Simons–Higgs system of rank 2 [Formula presented] over a flat torus, where m_1,l≥0, m_2,l≥0, (m_1,l,m_2,l)≠(0,0) for l=1,…,N, δ_p is the Dirac measure at p, K is a non-degenerate 2 × 2 matrix of the form K=1+a−a−b1+b. When a>−1, b>−1, and a+b>−1, Eqs (0.1) are expected to have three types solutions: topological, non-topological and mixed type solutions. Concerning the existence of various type solutions, there are requirements that a>0 and b>0, or a and b are close to 0 in the literature. It is still open for generic a and b. We partially answer this question and show that (0.1) possesses bubbling mixed type solutions provided that ɛ is small and (a,b) satisfies (1.17).