Uniqueness and stability of solutions to some elliptic problems.

Yao, Wei.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 52-58).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 2 --- Orbital stability without linear optical lattice --- p.12Chapter 2.1 --- Properties of single-spike bound states --- p.12Chapter 2.2 --- Proof of theorem 1.0.1 --- p.20Chapter 3 --- Orbital stability with linear optical lattice --- p.30Chapter 3.1 --- Properties of single-spike bound states --- p.30Chapter 3.2 --- Proof of theorem 1.0.2 --- p.33Chapter 3.3 --- Proof of theorem 1.0.3 --- p.34Chapter 3.4 --- Proof of theorem 1.0.4 --- p.37Chapter 4 --- Uniqueness for semilinear elliptic systems --- p.42Chapter 4.1 --- Proof of theorem 1.0.5 --- p.42Chapter 5 --- Appendix --- p.44Chapter 5.1 --- Appendix A --- p.44Chapter 5.2 --- Appendix B --- p.45Chapter 5.3 --- Appendix C --- p.4