哈密顿系统指标理论与多解问题

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