by Chin Pang Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 38-39). / Abstracts in English and Chinese. / Chapter 1 --- Main Results and Introduction --- p.4 / Chapter 1.1 --- Preliminaries --- p.5 / Chapter 2 --- The Linearized Operator in the Weighted Sobolev Spaces --- p.8 / Chapter 2.1 --- Weighted Sobolev Space and Some Useful Properties --- p.8 / Chapter 2.2 --- The Linearized Operator --- p.10 / Chapter 3 --- Reduction to Finite Dimensions --- p.19 / Chapter 4 --- Reduced Problem --- p.27 / Chapter 4.1 --- Proof of Theorem 1.1 --- p.27 / Chapter 4.2 --- Asymptotic Behavior of uE --- p.34 / Bibliography

Yeung Sik-ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 39-42). / Chapter 1 --- Introduction and Statement of the Results --- p.3 / Chapter 2 --- Maximum Principles and Comparison Theorems --- p.12 / Chapter 3 --- Pohozaev Identity and Symmetry for p-Laplacian when 1<p<2 --- p.18 / Chapter 4 --- Singularly Perturbed p-Laplacian Equation --- p.23 / Chapter 5 --- Appendix --- p.31 / Bibliography --- p.39

Cheung Ka Luen. / "December 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 95-101). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Yao, Wei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 52-58). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Orbital stability without linear optical lattice --- p.12 / Chapter 2.1 --- Properties of single-spike bound states --- p.12 / Chapter 2.2 --- Proof of theorem 1.0.1 --- p.20 / Chapter 3 --- Orbital stability with linear optical lattice --- p.30 / Chapter 3.1 --- Properties of single-spike bound states --- p.30 / Chapter 3.2 --- Proof of theorem 1.0.2 --- p.33 / Chapter 3.3 --- Proof of theorem 1.0.3 --- p.34 / Chapter 3.4 --- Proof of theorem 1.0.4 --- p.37 / Chapter 4 --- Uniqueness for semilinear elliptic systems --- p.42 / Chapter 4.1 --- Proof of theorem 1.0.5 --- p.42 / Chapter 5 --- Appendix --- p.44 / Chapter 5.1 --- Appendix A --- p.44 / Chapter 5.2 --- Appendix B --- p.45 / Chapter 5.3 --- Appendix C --- p.47

vi, 133 leaves / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1972

Thesis (Ph.D.) -- University of Adelaide, Dept. of Pure Mathematics, 1972.

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 195-197).

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Bibliography: p. 195-197.

Thesis (doctoral)--University of Bonn, 1988. / Includes bibliographical references (p. 108-109).

In the first part of this thesis, strong comparison theorems of Sturm's type are established for systems of second order quasilinear elliptic partial differential equations. The technique used leads to new oscillation and nonoscillation criteria for such systems. Some criteria are deduced from a comparison theorem, and others are derived by a direct variational method. Some of our results constitute extensions of known theorems to non-self-adjoint quasilinear systems. Application of these results to first order systems leads to criteria for the existence of conjugate points. In the second part, comparison theorems are obtained for elliptic differential operators of arbitrary even order. A description of the behaviour of the smallest eigenvalue for such operators is given under domain perturbations by means of Garding's inequality. New oscillation and nonoscillation criteria are obtained by variational methods. Specialization of our theorems to elliptic equations of fourth order, and to ordinary differential equations yields various generalizations of known results. / Science, Faculty of / Mathematics, Department of / Graduate