董玉君編寫的《哈密頓繫統指標理論與多解問題
(英文版)》的主要內容為線性繫統指標理論的建立及
其漸近線性繫統多解問題的研究。這些繫統包括達芬
方程、一維p-Laplacian方程、二階哈密頓繫統、一
階哈密頓繫統及其自伴算子方程等。與法國數學家
Ekeland的名著Convexity methods in
Hamiltonian mechanics及其龍以明院士的名著
Index theory for symplecticpaths with
applications主要討論哈密頓繫統周期解不同，本書
主要討論非周期解問題。

Preface
Chapter 1 An Overview
Chapter 2 Du±ng Equations(I)
2.1 Lazer-Leach's theorem
2.2 A classi cation 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 classi cation 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 iv Contents
6.2 P-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 P-nitions 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-index
8.3 Ekeland's type of index theory
8.4 Existence of solutions
8.5 Multiple solutions
8.6 A new reduced functional
8.7 The Morse index theory for a''(u*)
8.8 Proofs of Theorems 8.5.1 and 8.5.2
Bibliography
Index