哈密顿系统指标理论与多解问题 本书特色

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。

哈密顿系统指标理论与多解问题 目录

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

自然科学 数学 数学理论

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