Kong Yin To. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 53-55). / Abstracts in English and Chinese. / Chapter 1 --- On the Role of Robin Function in Some Singular Per- turbation Problems with Zero Mass --- p.4 / Chapter 1.1 --- Introduction --- p.4 / Chapter 1.2 --- Preliminary Results and Set-up of a Min-Max Scheme --- p.9 / Chapter 1.3 --- Proof of Theorem 1.1 --- p.25 / Chapter 2 --- On a Singularly Perturbed Dirichlet Problem in Con- vex Domain --- p.29 / Chapter 2.1 --- Introduction --- p.29 / Chapter 2.2 --- Preliminary Analysis --- p.33 / Chapter 2.3 --- Location of Multiple Peaks --- p.37 / Chapter 2.4 --- Proof of No Multiple-Peaked Solutions in Convex Do- mains --- p.48

Chiu Ho Man Edward. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 36-39). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Some Preliminary Analysis --- p.11 / Chapter 3 --- An Auxiliary Linear problem --- p.16 / Chapter 4 --- Construction of natural constraint --- p.22 / Chapter 5 --- Energy computation for reduced energy functional --- p.26 / Chapter 6 --- Proof of Theorem 1.1 --- p.29 / Bibliography --- p.36

Ao, Weiwei. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 92-97). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Spikes on Single Line-Segments --- p.12 / Chapter 2.1 --- Ansatz and sketch of the proof --- p.12 / Chapter 2.2 --- Linear theory --- p.15 / Chapter 2.3 --- The non linear projected problem --- p.20 / Chapter 2.4 --- Projection of the error and proof of Theorem 1.0.1 --- p.24 / Chapter 3 --- The triple junction solutions --- p.33 / Chapter 3.1 --- Approximate solutions --- p.33 / Chapter 3.2 --- linear and nonlinear projected problem --- p.35 / Chapter 3.3 --- Error estimates and the proof of theorem 1.0.2 --- p.35 / Chapter 4 --- Layer concentrations in three-dimensional domain --- p.45 / Chapter 4.1 --- Preliminaries and setting up the problem --- p.45 / Chapter 4.1.1 --- A linear model problem --- p.45 / Chapter 4.1.2 --- Setting up the problem in suitable coordinates --- p.53 / Chapter 4.2 --- The gluing procedure --- p.62 / Chapter 4.3 --- The invertibility of L2 --- p.65 / Chapter 4.4 --- Solving the nonlinear projected problem --- p.67 / Chapter 4.5 --- Estimates of the projection against ∇w and Z --- p.72 / Chapter 4.5.1 --- estimates for the projection of the error --- p.73 / Chapter 4.5.2 --- projection of terms involving φ --- p.78 / Chapter 4.5.3 --- projection of errors on the boundary --- p.80 / Chapter 4.6 --- "The system for (f1, f2, e):proof of the theorem" --- p.81

No description available.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1988. / Vita. Abstract. Includes bibliographical references (leaves 154-155). Also available via the Internet.

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Yi, Yingfei; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Verriest, Erik; Committee Member: Weiss, Howie. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1997. / Includes bibliographical references. Also available on the Internet.

No description available.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1996. / Vita. Abstract. Includes bibliographical references (leaves 90-92). Also available via the Internet.

Firstly, we establish the existence of a solution u epsilon concentrating along a curve Gammaepsilon near the non-degenerate Gamma, exponentially small in epsilon at any positive distance from the curve, provided epsilon is small and away from certain critical numbers. The concentrating curve Gammaepsilon will collapse to Gamma as epsilon → 0. / In this thesis, we consider the following problem 32Du-u+up= 0 and u>0 in W , 6u6n= 0 on 6W, where O is a bounded domain in R2 with smooth boundary, epsilon is a small positive parameter, nu denotes the outward normal of O and p > 1. Let Gamma be a straight line intersecting orthogonally with ∂O at exactly two points. We use the infinite dimensional Lyapunov-Schmidt reduction method, introduced by M. del Pino, M. Kowalczyk and J. Wei in [14], to deal with the non-invertibility caused by the critical eigenvalues of the linearized operator in the perturbed problems and then construct interior concentration layers near Gamma, which interact with the boundary. Moreover, the method of successive improvements of the approximation helps us decompose the interaction between the boundary and the interior layers. / Secondly, for any given integer N with N ≥ 2 and for small epsilon away from certain critical numbers, we construct another solution uepsilon exhibiting N concentration layers at mutual distances O(epsilon∣ ln epsilon∣), whose concentration set will approach the non-degenerate and non-minimal Gamma as epsilon → 0, provided that the exponent p ≥ 2. Asymptotic location of these layers is governed by a Toda type system. / Yang, Jun. / "July 2007." / Adviser: Juncheng Wei. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 129-136). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.