ON TODA SYSTEM WITH CARTAN MATRIX G2.

We consider the Toda system Δui + Σj=1²aijeuj = 4πγiδ0 in R², ∫R² euidx < ∞, for i = 1,2, where γi > −1, δ0 is the Dirac measure at 0, and the coefficients aij are of the Cartan matrix of rank 2: A2,B2(= C2),G2. Previously, the authors have gotten the classification and non-degeneracy results of solutions for Cartan matrix A2 and B2. In this paper, we consider the G2 case, and we completely classify the solutions and obtain the quantization result as well as the nondegeneracy of solutions for the G2 Toda system. [ABSTRACT FROM AUTHOR]