2,369 research outputs found
Two-parameter Sturm-Liouville problems
This paper deals with the computation of the eigenvalues of two-parameter
Sturm- Liouville (SL) problems using the Regularized Sampling Method, a method
which has been effective in computing the eigenvalues of broad classes of SL
problems (Singular, Non-Self-Adjoint, Non-Local, Impulsive,...). We have shown,
in this work that it can tackle two-parameter SL problems with equal ease. An
example was provided to illustrate the effectiveness of the method.Comment: 9 page
A note on the dependence of solutions on functional parameters for nonlinear sturm-liouville problems
We deal with the existence and the continuous dependence of solutions on functional
parameters for boundary valued problems containing the Sturm-Liouville equation.
We apply these result to prove the existence of at least one solution for a certain class of
optimal control problems
Analyticity and uniform stability of the inverse singular Sturm--Liouville spectral problem
We prove that the potential of a Sturm--Liouville operator depends
analytically and Lipschitz continuously on the spectral data (two spectra or
one spectrum and the corresponding norming constants). We treat the class of
operators with real-valued distributional potentials in the Sobolev class
W^{s-1}_2(0,1), s\in[0,1].Comment: 25 page
An inverse Sturm-Liouville problem with a fractional derivative
In this paper, we numerically investigate an inverse problem of recovering
the potential term in a fractional Sturm-Liouville problem from one spectrum.
The qualitative behaviors of the eigenvalues and eigenfunctions are discussed,
and numerical reconstructions of the potential with a Newton method from finite
spectral data are presented. Surprisingly, it allows very satisfactory
reconstructions for both smooth and discontinuous potentials, provided that the
order of fractional derivative is sufficiently away from 2.Comment: 16 pages, 6 figures, accepted for publication in Journal of
Computational Physic
On the isospectral problem of the dispersionless Camassa-Holm equation
We discuss direct and inverse spectral theory for the isospectral problem of
the dispersionless Camassa--Holm equation, where the weight is allowed to be a
finite signed measure. In particular, we prove that this weight is uniquely
determined by the spectral data and solve the inverse spectral problem for the
class of measures which are sign definite. The results are applied to deduce
several facts for the dispersionless Camassa--Holm equation. In particular, we
show that initial conditions with integrable momentum asymptotically split into
a sum of peakons as conjectured by McKean.Comment: 26 page
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