Geng Di. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 116-119). / Acknowledgement --- p.i / Abstract --- p.ii / Introduction --- p.iii / Part I --- p.1 / Chapter 1 --- Critical Dimension of a Semilinear Degenerate Elliptic Equation Involving Critical Sobolev-Hardy Exponent --- p.2 / Chapter 1.1 --- Introduction --- p.2 / Chapter 1.2 --- Non-existence (I) --- p.5 / Chapter 1.3 --- Non-existence (II) --- p.11 / Chapter 1.4 --- Existence --- p.13 / Chapter 1.5 --- Radial Symmetry of Solutions --- p.16 / Appendix A --- p.20 / Appendix B --- p.23 / Chapter 2 --- Critical Dimension of a Hessian Equation Involving Critical Ex- ponent --- p.27 / Chapter 2.1 --- Introduction --- p.27 / Chapter 2.2 --- Preliminary Results --- p.29 / Chapter 2.3 --- Existence Results --- p.32 / Chapter 2.4 --- Non-existence Results --- p.43 / Chapter 3 --- Absence of Critical Dimension for the Subelliptic Laplacian on the Heisenberg Group --- p.48 / Chapter 3.1 --- Introduction and Main Result --- p.48 / Chapter 3.2 --- Proof of the Theorem --- p.49 / Part2 --- p.55 / Chapter 4 --- Asymptotic Behavior for Weighted p-Laplace Equations Involv- ing Critical Growth on the Ball --- p.56 / Chapter 4.1 --- Introduction --- p.56 / Chapter 4.2 --- A Crucial Lemma --- p.59 / Chapter 4.3 --- Proof of the Main Theorems --- p.61 / Chapter 5 --- Asymptotics for a Semilinear Weighted Elliptic Equation In- volving Critical Sobolev-Hardy Exponent --- p.71 / Chapter 5.1 --- Introduction --- p.71 / Chapter 5.2 --- Some Preliminary Results --- p.73 / Chapter 5.3 --- A Crucial Estimate --- p.80 / Chapter 5.4 --- Proof of the Main Theorem --- p.85 / Appendix --- p.88 / Chapter 6 --- Asymptotics for Positive Solutions for a Biharmonic Equation Involving Critical Exponent --- p.93 / Chapter 6.1 --- Introduction --- p.93 / Chapter 6.2 --- Preliminary Results --- p.94 / Chapter 6.3 --- Pohozaev's identity and Green's Function --- p.98 / Chapter 6.4 --- A Crucial Lemma --- p.103 / Chapter 6.5 --- Proof of Main Theorem --- p.112 / Bibliography --- p.115
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_321576 |
| Date | January 1996 |
| Contributors | Geng, Di., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, xi, 119 leaves ; 30 cm. |
| 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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