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Title page

Chapter 1. Introduction

1.1. Background

1.2. Previous results

1.3. Main results

1.4. Sketch of the proof for the case 𝐴₂

1.5. Sketch of the proof for 𝐵₂ case

1.6. Organization of the paper

Chapter 2. Proof of Theorem 1.1 in the 𝐴₂ case

2.1. Functional formulation of the problem

2.2. First approximate solution

2.3. Invertibility of linearized operator

2.4. Improvements of the approximate solution: 𝑂(\ve) term

2.5. Next improvement of the approximate solution: 𝑂(\ve²) term

2.6. A nonlinear projected problem

2.7. Proof of Theorem 1.1 for 𝐴₂ under Assumption (i)

2.8. Proof of Theorem 1.1 for 𝐴₂ under Assumption (ii)

2.9. Proof of Theorem 1.1 for 𝐴₂ under Assumption (iii)

Chapter 3. Proof of Theorem 1.1 in the 𝐵₂ case

3.1. Functional formulation of the problem for 𝐵₂ case

3.2. Classification and non-degeneracy for 𝐵₂ Toda system

3.3. Invertibility of the linearized operator

3.4. Improvements of the approximate solution

3.5. Proof of Theorem 1.1 for 𝐵₂ under Assumption (i)

3.6. Proof of Theorem 1.1 for 𝐵₂ under Assumption (ii)

3.7. Proof of Theorem 1.1 for 𝐵₂ under Assumption (iii)

Chapter 4. Appendix

4.1. Classification and non-degeneracy of 𝐵₂ Toda system with singular sources

4.2. The calculations of the matrix 𝑄₁

4.3. The calculations of the matrix 𝑄₁

Bibliography

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