《哈密頓系統指標理論與多解問題（英文版）》是2014年科學出版社出版地 他圖書，作者是董玉君。
基本介紹
- 書名：哈密頓系統指標理論與多解問題（英文版）
- 作者：董玉君
- 定價：58.00
- 出版社：科學出版社
- 出版時間：2014年12月
語種：,內容簡介,圖書目錄,
語種：
標準書號：978-7-03-042542-3 裝幀：平裝
版本：101 開本：B5
責任編輯：李靜科,趙彥超 字數：210千字
讀者對象： 頁數：172
書類： 冊/包：
編輯部：數理
附註：
內容簡介
本書的主要內容為線性系統指標理論的建立及其漸近線性系統多解問題的研究。這些系統包括達芬方程、一維p-Laplacian方程、二階哈密頓系統、一階哈密頓系統及其自伴運算元方程等。與法國數學家Ekeland的名著ConvexitymethodsinHamiltonianmechanics及其龍以明院士的名著Indextheoryforsymplecticpathswithapplications主要討論哈密頓系統周期解不同，本書主要討論非周期解問題。
圖書目錄
Preface
Chapter 1 An Overview
Chapter 2 Du±ng Equations（Ⅰ）
2.1 Lazer—Leach's theorem
2.2 A classiˉcation theory
2.3 A generalization of Lazer—Leach's theorem
2.4 Landesman—Lazer's condition
Chapter 1 An Overview
Chapter 2 Du±ng Equations（Ⅰ）
2.1 Lazer—Leach's theorem
2.2 A classiˉcation theory
2.3 A generalization of Lazer—Leach's theorem
2.4 Landesman—Lazer's condition
2.5 Nontrivial solutions
2.6 Sturm—Liouville BVPs
Chapter 3 Du±ng Equations（Ⅱ）
3.1 Positive linear Du±ng equations
3.2 Associated Leray—Schauder degrees
3.3 Asymptotically positive linear Du±ng equations
3.4 Limiting cases
3.5 Proof of Theorem 3.4.1
3.6 Proof of Theorem 3.4.2
3.7 Open questions
Chapter 4 One—dimensional p—Laplacian Equations
4.1 p—triangle functions
4.2 A classiˉcation theory
4.3 Associated Leray—Schauder degrees
4.4 Solutions of asymptotically homogeneous equations
4.5 Related problems
Chapter 5 Second Order Hamiltonian Systems
5.1 Index theory
5.2 Relative Morse index and topological degree
5.3 Existence of solutions
5.4 Multiple solutions for symmetric Hamiltonian systems
5.5 Three solution theorems
Chapter 6 First Order Hamiltonian Systems
6.1 Index theory
6.21—index and relative Morse index
6.3 Existence of solutions
6.4 Multiple solutions for symmetric Hamiltonian systems
6.5 Ekeland's index and Long's index
Chapter 7 Operator Equations（Ⅰ）
7.1 Deˉnitions for index and nullity
7.2 Properties for index and nullity
7.3 Solutions of operator equations
7.4 Multiple solutions for symmetric operator equations
7.5 Three solution theorems
Chapter 8 Operator Equations（Ⅱ）
8.1 Index theory
8.2 P—in
8.3Ekeland's type of index theory
8.4Existence of solutions
8.5Multiple solutions
8.6A new reduced functional
8.7The Morse index theory for a''（u*）
8.8 Proofs of Theorems 8.5.1 and 8.5.2
Bibliography
Index
2.6 Sturm—Liouville BVPs
Chapter 3 Du±ng Equations（Ⅱ）
3.1 Positive linear Du±ng equations
3.2 Associated Leray—Schauder degrees
3.3 Asymptotically positive linear Du±ng equations
3.4 Limiting cases
3.5 Proof of Theorem 3.4.1
3.6 Proof of Theorem 3.4.2
3.7 Open questions
Chapter 4 One—dimensional p—Laplacian Equations
4.1 p—triangle functions
4.2 A classiˉcation theory
4.3 Associated Leray—Schauder degrees
4.4 Solutions of asymptotically homogeneous equations
4.5 Related problems
Chapter 5 Second Order Hamiltonian Systems
5.1 Index theory
5.2 Relative Morse index and topological degree
5.3 Existence of solutions
5.4 Multiple solutions for symmetric Hamiltonian systems
5.5 Three solution theorems
Chapter 6 First Order Hamiltonian Systems
6.1 Index theory
6.21—index and relative Morse index
6.3 Existence of solutions
6.4 Multiple solutions for symmetric Hamiltonian systems
6.5 Ekeland's index and Long's index
Chapter 7 Operator Equations（Ⅰ）
7.1 Deˉnitions for index and nullity
7.2 Properties for index and nullity
7.3 Solutions of operator equations
7.4 Multiple solutions for symmetric operator equations
7.5 Three solution theorems
Chapter 8 Operator Equations（Ⅱ）
8.1 Index theory
8.2 P—in
8.3Ekeland's type of index theory
8.4Existence of solutions
8.5Multiple solutions
8.6A new reduced functional
8.7The Morse index theory for a''（u*）
8.8 Proofs of Theorems 8.5.1 and 8.5.2
Bibliography
Index
