Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Ao, Weiwei. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 178-186). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Interior Spike Solutions for Lin-Ni-Takagi Problem --- p.7 / Chapter 1.1.1 --- Background and Main Results --- p.7 / Chapter 1.1.2 --- Sketch of the Proof of Theorem 1.1.1 --- p.12 / Chapter 1.2 --- The A2 and B2 Chern-Simons System --- p.14 / Chapter 1.2.1 --- Background --- p.14 / Chapter 1.2.2 --- Previous Results --- p.19 / Chapter 1.2.3 --- Main Results --- p.20 / Chapter 1.2.4 --- Sketch of the Proof for A₂ Case --- p.21 / Chapter 1.2.5 --- Sketch of the Proof for B₂ Case --- p.26 / Chapter 1.3 --- Organization of the Thesis --- p.27 / Chapter 2 --- The Lin-Ni-Takagi Problem --- p.29 / Chapter 2.1 --- Notation and Some Preliminary Analysis --- p.29 / Chapter 2.2 --- Linear Theory --- p.35 / Chapter 2.3 --- The Non Linear Projected Problem --- p.40 / Chapter 2.4 --- An Improved Estimate --- p.43 / Chapter 2.5 --- The Reduced Problem: A Maximization Procedure --- p.50 / Chapter 2.6 --- Proof of Theorem 1.1.1 --- p.58 / Chapter 2.7 --- More Applications and Some Open Problems --- p.60 / Chapter 3 --- The Chern-Simons System --- p.66 / Chapter 3.1 --- Proof of Theorem 1.2.1 in the A₂ Case --- p.66 / Chapter 3.1.1 --- Functional Formulation of the Problem --- p.66 / Chapter 3.1.2 --- First Approximate Solution --- p.68 / Chapter 3.1.3 --- Invertibility of Linearized Operator --- p.72 / Chapter 3.1.4 --- Improvements of the Approximate Solution: O(ε) Term --- p.76 / Chapter 3.1.5 --- Next Improvement of the Approximate Solution: O(ε²) Term --- p.78 / Chapter 3.1.6 --- A Nonlinear Projected Problem --- p.82 / Chapter 3.1.7 --- Proof of Theorem 1.2.1 for A₂ under Assumption (i) --- p.85 / Chapter 3.1.8 --- Proof of Theorem 1.2.1 for A₂ under Assumption (ii) --- p.94 / Chapter 3.1.9 --- Proof of Theorem 1.2.1 for A₂ under Assumption (iii) --- p.99 / Chapter 3.2 --- Proof of Theorem 1.2.1 in the B₂ Case --- p.100 / Chapter 3.2.1 --- Functional Formulation of the Problem for B₂ Case --- p.100 / Chapter 3.2.2 --- Classi cation and Non-degeneracy for B₂ Toda system --- p.101 / Chapter 3.2.3 --- Invertibility of Linearized Operator --- p.105 / Chapter 3.2.4 --- Improvements of the Approximate Solution --- p.106 / Chapter 3.2.5 --- Proof of Theorem 1.2.1 for B₂ under Assumption (i) --- p.112 / Chapter 3.2.6 --- Proof of Theorem 1.2.1 for B₂ under Assumption (ii) --- p.122 / Chapter 3.2.7 --- Proof of Theorem 1.2.1 for B₂ under Assumption (iii) --- p.127 / Chapter 3.3 --- Open Problems --- p.128 / Chapter 4 --- Appendix --- p.129 / Chapter 4.1 --- B₂ and G₂ Toda System with Singular Source --- p.129 / Chapter 4.1.1 --- Case 1: B₂ Toda system with singular source --- p.130 / Chapter 4.1.2 --- Case 2: G₂ Toda system with singular source --- p.136 / Chapter 4.2 --- The Calculations of the Matrix Q₁ --- p.148 / Chapter 4.3 --- The Calculations of the Matrix Q₁ --- p.169 / Bibliography --- p.178
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328135 |
| Date | January 2013 |
| Contributors | Ao, Weiwei., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (186 leaves) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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