About: Atkinson–Mingarelli theorem

An Entity of Type: WikicatOrdinaryDifferentialEquations, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In applied mathematics, the Atkinson–Mingarelli theorem, named after Frederick Valentine Atkinson and A. B. Mingarelli, concerns eigenvalues of certain Sturm–Liouville differential operators. In the simplest of formulations let p, q, w be real-valued piecewise continuous functions defined on a closed bounded real interval, I = [a, b]. The function w(x), which is sometimes denoted by r(x), is called the "weight" or "density" function. Consider the Sturm–Liouville differential equation The boundary conditions under consideration here are usually called and they are of the form:

Property Value
dbo:abstract
  • In applied mathematics, the Atkinson–Mingarelli theorem, named after Frederick Valentine Atkinson and A. B. Mingarelli, concerns eigenvalues of certain Sturm–Liouville differential operators. In the simplest of formulations let p, q, w be real-valued piecewise continuous functions defined on a closed bounded real interval, I = [a, b]. The function w(x), which is sometimes denoted by r(x), is called the "weight" or "density" function. Consider the Sturm–Liouville differential equation where y is a function of the independent variable x. In this case, y is called a solution if it is continuously differentiable on (a,b) and (p y′)(x) is piecewise continuously differentiable and y satisfies the equation at all except a finite number of points in (a,b). The unknown function y is typically required to satisfy some boundary conditions at a and b. The boundary conditions under consideration here are usually called and they are of the form: where the , i = 1, 2 are real numbers. We define (en)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 34665293 (xsd:integer)
dbo:wikiPageLength
  • 3882 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1029792859 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dcterms:subject
rdf:type
rdfs:comment
  • In applied mathematics, the Atkinson–Mingarelli theorem, named after Frederick Valentine Atkinson and A. B. Mingarelli, concerns eigenvalues of certain Sturm–Liouville differential operators. In the simplest of formulations let p, q, w be real-valued piecewise continuous functions defined on a closed bounded real interval, I = [a, b]. The function w(x), which is sometimes denoted by r(x), is called the "weight" or "density" function. Consider the Sturm–Liouville differential equation The boundary conditions under consideration here are usually called and they are of the form: (en)
rdfs:label
  • Atkinson–Mingarelli theorem (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:knownFor of
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is dbp:knownFor of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License