zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A uniqueness theorem for inverse eigenparameter dependent Sturm-Liouville problems. (English) Zbl 0890.34022

This paper deals with the inverse spectral problem for a regular Sturm-Liouville problem with boundary conditions depending on the eigenvalue parameter. More exactly, a uniqueness theorem is proved for second order boundary eigenvalue problems

-y '' +qy=λyon[0,1],
cosαy(0)+sinαy ' (0)=0,(aλ+b)y(1)=(cλ+d)y ' (1)·

It is assumed that the potential q is integrable, α(0,π), ad-bc>0 and c0. It is shown that two problems of the above form for which the eigenvalues and suitable norming constants coincide must have equal potentials. This result is an extension of a well-known theorem of Gel’fand and Levitan for Sturm-Liouville problems with standard boundary conditions to the interesting case of boundary conditions containing the eigenvalue parameter linearly.

MSC:
34B24Sturm-Liouville theory
34A55Inverse problems of ODE