𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On an inverse eigenvalue problem for a semilinear Sturm–Liouville operator

✍ Scribed by Peter Zhidkov

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
188 KB
Volume
68
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

The following problem is considered:

where λ is a spectral parameter. The inverse problem is studied: a subsequence λ n → +∞ of the sequence of eigenvalues is given and odd f is the unknown quantity. A description of the whole class of solutions of this problem is obtained. In addition, it is proved that there exists at most one function f such that an auxiliary function is nondecreasing.

📜 SIMILAR VOLUMES

An inverse problem for Sturm–Liouville d
An inverse problem for Sturm–Liouville differential operators on A-graphs
✍ V. Yurko 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 267 KB

An inverse problem of spectral analysis is studied for Sturm-Liouville differential operators on a A-graph with the standard matching conditions for internal vertices. The uniqueness theorem is proved, and a constructive solution for this class of inverse problems is obtained.

An Oscillation Theorem for a Sturm -Liou
An Oscillation Theorem for a Sturm -Liouville Eigenvalue Problem
✍ Martin Bohner 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 244 KB

We consider a certain Sturm -Liouville eigenvalue problem with self-adjoint and non ~ separated boundary conditions. We derive an explicit formula for the oscillation number of any given eigenfunction. 1991 Mathematics Subject Classification. 34 C 10. Keywords and phrases. Oscillation number, index

An interior inverse problem for the Stur
An interior inverse problem for the Sturm–Liouville operator with discontinuous conditions
✍ Chuan-Fu Yang; Xiao-Ping Yang 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 355 KB

In this work, we study the inverse problem for the Sturm-Liouville operator -D 2 + q with discontinuity boundary conditions inside a finite closed interval. Using spectral data of a kind, it is shown that the potential function q(x) can be uniquely determined by a set of values of eigenfunctions at