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醉染图书STURM-LIOUVILLE问题的几何结构(英文版)9787030619853
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Chapter 1 Basic on Sturm-Liouville Problems
1.1 Classes of Sturm-Liouville Problems
1.2 Characteristic Function
1.3 Equations with Piece-Wise Constant Coeffcients
1.4 Sturms Comparison Theorem and Prufer Transformation
Chapter 2 Differentiable Manifolds and Lie Groups
2.1 Differentiable Manifolds
2.2 Differentiable Maps and Tangent Vectors
. Complex Manifolds
2.4 Lie Groups
Chapter 3 Geometric Structures on Spaces of Boundary Conditions
3.1 Spaces of Boundary Conditions
3.2 Characteristic Curve and Surfaces
3.3 Di.erentiability of Continuous Eigenvalue Branches
3.4 Analyticity of Continuous Eigenvalue Branches
Chapter 4 Inequalities among Eigenvalues
4.1 More on Characteristic Function
4.2 Asymptotic Analysis of Fundamental Matrix
4.3 Inequalities among Eigenvalues for any coupled self-adjoint Boundary Condition
4.4 Ranges of λn on BR and BC
4.5 The Relationship among Three Multiplicities of a Differential Operators Eigenvalue
Chapter 5 Dependence of the n-th Eigenvalue on the Sturm-Liouville Problem
5.1 Continuity Principle
5.2 Continuous Dependence of on the Differential Equation
5.3 Discontinuity of λn
5.4 Comments on Di.erentiability of λn
5.5 The Index Problem for Eigenvalues for Coupled Boundary Conditions
Appendix A Fist-Order Linear Differential Equations
A.1 Existence and Uniqueness of Solution
A.2 Rank of a Solution and Variation of Parameters
A.3 Continuous Dependence of Solution on Problem
References
Index
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