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21.
Paul A. Binding Patrick J. Browne Bruce A. Watson 《Journal of Mathematical Analysis and Applications》2002,271(2):383-408
Inverse Sturm-Liouville problems with indefinite weight are considered. Theorems analogous to those of both Hochstadt and Gelfand-Levitan are proved. As a sample result, under suitable symmetry conditions, we show that half of one spectrum suffices to determine the potential function uniquely. 相似文献
22.
We consider one-dimensional p-Laplacian eigenvalue problems of the form
23.
A class of two-parameter eigenvalue problems involving generally nonselfadjoint and unbounded operators is studied. A basis for the root subspace at a geometrically simple eigenvalue of Fredholm type is computed in terms of the underlying two-parameter system. Comparison with Faierman's work on two-parameter boundary value problems of Sturm-Liouville type is given as an application.
24.
25.
Uwe Karst Norbert Binding Karl Cammann Ute Witting 《Fresenius' Journal of Analytical Chemistry》1993,345(1):48-52
Summary The influence of nitrogen oxides on the practicability and accuracy of the determination of aldehydes and ketones in air samples using the DNPH-method was examined. Nitrogen dioxide reacts with 2,4-dinitrophenylhydrazine and the reaction products were identified as 2,4-dinitrophenylazide (main product) and 2,4-dinitrochlorobenzene (by-product). They have a similar chromatographic behaviour in high performance liquid chromatography (HPLC) as formaldehyde-2,4-DNP-hydrazone. The chromatographic separation of the reaction products and formaldehyde-2,4-dinitrophenylhydrazone was performed using different gradient systems. Problems which occur in nitrogen dioxide-containing air samples are discussed. 相似文献
26.
Paul A. Binding Patrick J. Browne Bruce A. Watson 《Transactions of the American Mathematical Society》2002,354(10):4043-4065
The Sturm-Liouville equation
is considered subject to the boundary conditions
We assume that is positive and that is piecewise continuous and changes sign at its discontinuities. We give asymptotic approximations up to for , or equivalently up to for , the eigenvalues of the above boundary value problem.
is considered subject to the boundary conditions
We assume that is positive and that is piecewise continuous and changes sign at its discontinuities. We give asymptotic approximations up to for , or equivalently up to for , the eigenvalues of the above boundary value problem.
27.
Double variational principles are established for eigenvalues of a (norm) continuous self-adjoint operator valued functionL defined on a real interval [, [.L() is not required to be definite for any . Applications are made to linear, quadratic and rational functionsL.This author acknowledges support from NSERC of Canada and the I.W. Killam Foundation.This author was supported by the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 12176-MAT. 相似文献
28.
Inverse SturmLiouville problems with eigenparameter-dependentboundary conditions are considered. Theorems analogous to thoseof both Hochstadt and Gelfand and Levitan are proved. In particular, let ly = (1/r)((py')'+qy), ,
where det = > 0, c 0, det > 0, t 0 and (cs + dr au tb)2 < 4(cr ta)(ds ub). Denoteby (l; ; ) the eigenvalue problem ly = y with boundary conditionsy(0)cos+y'(0)sin = 0 and (a+b)y(1) = (c+d)(py')(1). Define (; ; ) as above but with l replacedby . Let wn denote the eigenfunctionof (l; ; ) having eigenvalue n and initial conditions wn(0)= sin and pw'n(0) = cos and let n = awn(1)+cpw'n(1).Define n and n similarly. As sample results, it is proved that if (l; ; ) and (; ; ) have the same spectrum, and (l;; ) and (; ; ) have the samespectrum or for all n, thenq/r = /. 相似文献
29.
Paul Binding Lyonell Boulton Patrick J. Browne 《Journal of Computational and Applied Mathematics》2007
Singular Sturm–Liouville problems for -y″+qy=λy on (0,∞) are studied for potentials q which are bounded below and satisfy Mol?anov's necessary and sufficient condition for discrete spectrum. A Prüfer angle approach is given for eigenvalue location and eigenfunction oscillation, paralleling that for the regular case. In particular, the eigenvalues are characterized by a “right-hand boundary condition” even though q is of limit point type. 相似文献
30.
Paul Binding 《Journal of Mathematical Analysis and Applications》1984,102(1):233-243
The multiparameter eigenvalue problem Wm(λ) xm = xm, , m = 1,…, k, where /gl /gE k, xm is a nonzero element of the separable Hilbert space Hm, and Tm and Vmn are compact symmetric is studied. Various properties, including existence and uniqueness, of λ = λi ? k for which the imth greatest eigenvalue of Wm(λi) equals one are proved. “Right definiteness” is assumed, which means positivity of the determinant with (m, n)th entry (ym, Vmnym) for all nonzero ym?Hm, m = 1 … k. This gives a “Klein oscillation theorem” for systems of an o.d.e. satisfying a definiteness condition that is usefully weaker than in previous such results. An expansion theorem in terms of the corresponding eigenvectors xmi is also given, thereby connecting the abstract oscillation theory with a result of Atkinson. 相似文献