ISBN:9787030423577
书籍目录
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
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
作者简介
本书的主要内容为线性系统指标理论的建立及其渐近线性系统多解问题的研究。这些系统包括达芬方程、一维p-Laplacian方程、二阶哈密顿系统、一阶哈密顿系统及其自伴算子方程等。与法国数学家Ekeland的名著ConvexitymethodsinHamiltonianmechanics及其龙以明院士的名著Indextheoryforsymplecticpathswithapplications主要讨论哈密顿系统周期解不同,本书主要讨论非周期解问题。