A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
On Sturm's separation theorem

1972
*
Canadian mathematical bulletin
*

The classical

doi:10.4153/cmb-1972-086-7
fatcat:mxbeyblvpnbjnmz3ttprrg5fsu
*theorem*(cf. ... In case y(a)=0, does the separation*theorem*hold? A complete answer to this question is given in*Theorem*1 below, and an application of the extended*theorem*is given in*Theorem*2. 2. ...##
###
A generalization of Sturm's comparison theorem
[article]

2021
*
arXiv
*
pre-print

This result is based on a, so called, concept of "null-classes", and is a generalization of

arXiv:2005.12538v3
fatcat:rn2rdj7ysnhjddo7uxda547o5m
*Sturm's*comparison*theorem*. ... The Riccati equation method is used to establish a new comparison*theorem*for systems of two linear first order ordinary differential equation. ... The*Sturm's*famous comparison*theorem*states (see [1] , p. 334)*Theorem*1.1 (Sturm). ...##
###
Sturm's theorem on zeros of linear combinations of eigenfunctions
[article]

2018
*
arXiv
*
pre-print

Motivated by recent questions about the extension of Courant's nodal domain

arXiv:1706.08247v4
fatcat:4xiq7t3pjbahhes7vz7v233wna
*theorem*, we revisit a*theorem*published by C. ... Although not specialists in History of Sciences, we have tried to put these*theorems*into the context of nineteenth century mathematics. ...*Sturm's*proof of*Theorem*1.3. ...##
###
The converse of Sturm's Separation Theorem
[article]

2021
*
arXiv
*
pre-print

We show that

arXiv:2109.06953v1
fatcat:b64our27jbgu3glbiebziuwijm
*Sturm's*classical separation*theorem*on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the ... This is the actual converse of*Sturm's*Separation*Theorem*. ... To the best of our knowledge, a converse of*Sturm's*Separation*Theorem*has not been addressed. ...##
###
A generalization of Sturm's comparison theorem

1966
*
Journal of Mathematical Analysis and Applications
*

INTRODUCTION Comparison

doi:10.1016/0022-247x(66)90105-3
fatcat:rzmogrnzy5en3ilcndki4gkyai
*theorems*of*Sturm's*type will be obtained for a pair of linear self-adjoint elliptic partial differential equations. ... following example illustrates that*Theorem*5 is more general than Kreith's*theorem*. ...##
###
Sturm's theorem on the zeros of sums of eigenfunctions: Gelfand's strategy implemented
[article]

2018
*
arXiv
*
pre-print

In the second section "Courant-Gelfand

arXiv:1807.03990v3
fatcat:7rquptykvnfzhe455zy6lbta7e
*theorem*" of his last published paper (Topological properties of eigenoscillations in mathematical physics, Proc. ... Courant 2 partly generalized Assertion 2, in*Sturm's**theorem*, to higher dimensions.*Theorem*1.3. ... This is a weak form of*Sturm's*upper bound, Assertion 3a in*Theorem*1.1. ...##
###
A generalization of Sturm's separation theorem

1970
*
Proceedings of the American Mathematical Society
*

A comparison

doi:10.1090/s0002-9939-1970-0255959-3
fatcat:aot35mxyp5gdfl6qjim34u2oc4
*theorem*for linear equations and a separation*theorem*for quasilinear equations are then obtained as applications. ... A Sturmian separation*theorem*is established for elliptic-parabolic equations with minimal assumptions on the coefficients and none on the regularity of the domain. ... The contradiction establishes the*theorem*. The separation*theorem*now follows for operators for which there exists a function/ such that L(/) <0. ...##
###
Sturm's theorem for equations with delayed argument

1994
*
Georgian Mathematical Journal
*

*Sturm's*type

*theorems*on separation of zeros of solutions are proved for the second order linear differential equations with delayed argument. ... It is also known [1] that nonvanishing of the Wronskian is equivalent to the validity of

*Sturm's*

*theorem*about separation of zeros. ... This article deals with the extension of the

*Sturm's*

*theorem*to equation (1) with delayed argument. The first result of this type was obtained by N.V.Azbelev [1] . ...

##
###
A New Proof of Sturm's Theorem via Matrix Theory
[article]

2021
*
arXiv
*
pre-print

Therefore, this paper offers a new proof of

arXiv:2110.15364v1
fatcat:sbxokwg4bjdlhcovphocjk6vya
*Sturm's**theorem*using matrix theory. ... By the classical*Sturm's**theorem*, the number of distinct real roots of a given real polynomial $f(x)$ within any interval $(a,b]$ can be expressed by the number of variations in the sign of the Sturm chain ...*Theorem*(*Sturm's**Theorem*[1] ). ...##
###
Note on the practical application of Sturm's theorem

1906
*
Bulletin of the American Mathematical Society
*

NOTE ON

doi:10.1090/s0002-9904-1906-01348-9
fatcat:v5ua23e335gpxffiswwxd6akky
*STURM'S**THEOREM*. [April, As three particular solutions, take S=2U/(u+ v)-Cr', v = 2V l /(u + v)-V' u Ç=2VJ(u + v)-V 2 . ... NOTE ON THE PRACTICAL APPLICATION OF*STURM'S**THEOREM*. BY J. E. WRIGHT, M.A. Neue Beitrdge zur Frage des mathematischen und physikalischen Unterrichts an den höheren Schulen. F. KLEIN und E. Teil I. ...##
###
358. Note on Sturm's Theorem in the Theory of Equations

1911
*
Mathematical Gazette
*

Note on

doi:10.2307/3602856
fatcat:w4f3gr7ribfcjeo7tosrrotfxq
*Sturm's**theorem*in the theory of equations. ... Note on*Sturm's**theorem*in the theory of equations. ...##
###
NOTE ON STURM'S THEOREM FOR A STRONGLY ELLIPTIC SYSTEMS

1973
*
Demonstratio Mathematica
*

Janusz Wqsowski
NOTE ON

doi:10.1515/dema-1973-0303
fatcat:rkhjnvbrcjg3ta2efzmfa5depq
*STURM'S**THEOREM*FOR A STRONGLY ELLIPTIC SYSTEMS In this paper*Sturm's**Theorem*(see [l] , [2] , [5] ) for a linear strongly elliptic systems of second order is given. ...##
###
Sturm's theorem on zeros of linear combinations of eigenfunctions

2018
*
Expositiones mathematicae
*

Motivated by recent questions about the extension of Courant's nodal domain

doi:10.1016/j.exmath.2018.10.002
fatcat:72r7a2i3ifeb7d3djg6qfcscwa
*theorem*, we revisit a*theorem*published by C. ... Although not specialists in History of Sciences, we have tried to replace these*theorems*into the context of nineteenth century mathematics. ... We refer to [5, 30] for the relationships between*Theorem*1.3 and*Sturm's**theorem*on the number of real roots of real polynomials.*Sturm's*motivations. ...##
###
An analogue of Sturm's theorem for Hilbert modular forms

2013
*
Algebra & Number Theory
*

We prove an analogue of

doi:10.2140/ant.2013.7.1001
fatcat:5qnu4x3enfhjbbahgpr375ffcm
*Sturm's*result for Hilbert modular forms associated to totally real number fields. ... An analogue of*Sturm's**theorem*for Hilbert modular forms ... The reason why we call*Theorem*1 an "analogue" of*Sturm's**theorem*is that the constant κ includes a strange constant C. ...##
###
On an inverse spectral problem and a generalized Sturm's nodal theorem for nonlinear boundary value problems
[article]

2018
*
arXiv
*
pre-print

The key outcome of this relationship is a generalized

arXiv:1809.00229v1
fatcat:igyk7buoh5ey5kttck3jyuix3u
*Sturm's*nodal*theorem*for the nonlinear boundary value problems. ... ., the proofs of assertions (2 o ), (3 o ) immediately follow from (2 o ), (3 o )*Theorem*1. ... We emphasize that this result is nothing more than a generalization of the well known*Sturm's*nodal*theorem*to the nonlinear problem. ...
« Previous

*Showing results 1 — 15 out of 2,115 results*