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This paper studies solutions to a singular SU (3) Toda system with linear source terms on a compact Riemann surface with smooth boundaries. We establish the existence of solutions when the parameters are not critical, assuming that Euler characteristic () <1 via analyzing the sublevels. Furthermore, we find a sufficient condition that ensures multiple solutions for generic potentials by Morse inequalities and a transversality theorem.
Zhengni Hu (Tue,) studied this question.