Continuation Principle and Bernstein Boundary Value Problem

• Main Authors: Sheng-Yarng Chen, 陳生洋
• Other Authors: Chung-Wei Ha
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/46431171581744990635

碩士 === 國立清華大學 === 數學系 === 87 === Abstract This thesis is a study of the continuation method applied to the Bernstein boundary value problem.BasedonLeray-Schauder degree theory, a continuation principle and some of its consequences are given in \S III. A brief sketch of the Leray-Schauder degree theory is given in \S II. We refer to Zeidler [10] for a modern treatment of the degree theory. In \S IV we apply the results obtained in \S III to the structure of the solution set of the Bernstein problem recently generalized in [5]. For the proofs of the topological results in \S III we make essential use of the following separation theorem for compact sets known as Whyburn lemma (see Whyburn [9], p\. 12 and Zeidler [10], p\. ~636).