منابع مشابه
Reflectionless Sturm-Liouville Equations
We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, ...
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We extend the idea of Jodeit and Levitan [3] for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are found.
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Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.
متن کاملSturm-liouville Eigenvalue Characterizations
We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...
متن کاملRandom Sturm-Liouville operators
Selfadjoint Sturm-Liouville operators Hω on L2(a, b) with random potentials are considered and it is proven, using positivity conditions, that for almost every ω the operator Hω does not share eigenvalues with a broad family of random operators and in particular with operators generated in the same way as Hω but in L2(ã, b̃) where (ã, b̃) ⊂ (a, b).
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1988
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1988.102249