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 parison theorem and prufer transformation chapter 2 differentiable manifolds and lie grou 2.1 differentiable manifolds 2.2 differentiable ma and tangent vectors 2.3 plex manifolds 2.4 lie grou 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 ments 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 estence 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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