A Prüfer approach to half-linear Sturm-Liouville problems
نویسندگان
چکیده
منابع مشابه
Sturm-liouville Problems
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.
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Left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions are studied. A characterization is given in terms of right-definite problems, a concrete and “natural” indexing scheme for the eigenvalues is proposed. Pruefer transformation techniques can be used to establish the existence of and to give a characterization for the eigenvalues in the case...
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The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on boundary points. The derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. This for arbitrary (separated or coupled) self-adjoint regular boundary conditions. In addition, as the length of the interval shrinks to zero all higher eigenvalues march o...
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A new algorithm is proposed for solving the inverse Sturm–Liouville problem of reconstructing a symmetric potential from eigenvalues. It uses Numerov’s method instead of the second order method of the related algorithm of Fabiano, Knobel and Lowe. An extension by Andrew and Paine of the asymptotic correction technique of Paine, de Hoog and Anderssen is the key to the success of the new algorith...
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We describe a new algorithm to compute the eigenvalues of singular Sturm-Liouville problems with separated self-adjoint boundary conditions for both the limit-circle nonoscillatory and oscillatory cases. Also described is a numerical code implementing this algorithm and how it compares with SLEIGN. The latter is the only effective general purpose software available for the computation of the ei...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1998
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500019908