哈密顿系统指标理论与多解问题

PrefaceChapter 1 An OverviewChapter 2 Du±ng Equations(I)2.1 Lazer-Leach's theorem2.2 A classi?cation theory2.3 A generalization of Lazer-Leach's theorem2.4 Landesman-Lazer's condition2.5 Nontrivial solutions2.6 Sturm-Liouville BVPsChapter 3 Du±ng Equations(II)3.1 Positive linear Du±ng equations3.2 Associated Leray-Schauder degrees3.3 Asymptotically positive linear Du±ng equations3.4 Limiting cases3.5 Proof of Theorem 3.4.13.6 Proof of Theorem 3.4.23.7 Open questionsChapter 4 One-dimensional p-Laplacian Equations4.1 p-triangle functions4.2 A classi?cation theory4.3 Associated Leray-Schauder degrees4.4 Solutions of asymptotically homogeneous equations4.5 Related problemsChapter 5 Second Order Hamiltonian Systems5.1 Index theory5.2 Relative Morse index and topological degree5.3 Existence of solutions5.4 Multiple solutions for symmetric Hamiltonian systems5.5 Three solution theoremsChapter 6 First Order Hamiltonian Systems6.1 Index theoryiv Contents6.2 ?-index and relative Morse index6.3 Existence of solutions6.4 Multiple solutions for symmetric Hamiltonian systems6.5 Ekeland's index and Long's indexChapter 7 Operator Equations(I)7.1 De?nitions for index and nullity7.2 Properties for index and nullity7.3 Solutions of operator equations7.4 Multiple solutions for symmetric operator equations7.5 Three solution theoremsChapter 8 Operator Equations(II)8.1 Index theory8.2 P-in

《哈密顿系统指标理论与多解问题（英文版）》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Convexity methods in Hamiltonian mechanics及其龙以明院士的名著Index theory for symplecticpaths with applications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。