Four-Vertex Theorems, Sturm Theory and Lagrangian Singularities

2004 ◽  
Vol 7 (3) ◽  
pp. 223-237 ◽  
Author(s):  
Ricardo Uribe-Vargas
Keyword(s):  
Lagrangian Singularities ◽  
Sturm Theory

Symmetric lagrangian singularities and Gauss maps of theta divisors

1991 ◽  
pp. 1-26
Author(s):  
Malcolm R. Adams ◽  
Clint McCrory ◽  
Theodore Shifrin ◽  
Robert Varley
Keyword(s):  
Gauss Maps ◽  
Lagrangian Singularities

scholarly journals Theorem on six vertices of a plane curve via Sturm theory

1997 ◽  
pp. 257-266 ◽  
Author(s):  
L. Guieu ◽  
E. Mourre ◽  
V. Yu Ovsienko
Keyword(s):  
Plane Curve ◽  
Sturm Theory

scholarly journals Some sturm theory

1981 ◽  
Vol 39 (1) ◽  
pp. 296-296
Author(s):  
Walter Leighton
Keyword(s):  
Sturm Theory

Multiparameter Sturm theory

1984 ◽  
Vol 99 (1-2) ◽  
pp. 173-184 ◽  
Author(s):  
Paul Binding ◽  
Patrick J. Browne
Keyword(s):  
Elliptic Partial Differential Equation ◽  
Comparison Theorems ◽  
Unified Theory ◽  
Focal Points ◽  
The Matrix ◽  
Sturm Liouville ◽  
Left And Right ◽  
Image Position ◽  
Completeness Of Eigenfunctions ◽  
Sturm Theory

SynopsisLet Sturm–Liouville problemswith continuous coefficients and appropriate boundary conditions, be coupled by the eigenvalue λ = (λ1, … λk). When k = 1, there are various oscillation, perturbation and comparison theorems concerning existence and continuous or monotonic dependence of eigenvalues, eigenfunctions and their zeros (i.e. focal points).We attempt a unified theory for such results, valid for general fc, under conditions known as "left" and “right” definiteness. A representative result may be stated loosely as follows: if LD holds then (elementwise) monotonic dependence of p, q and the matrix [ars] forces monotonic dependence of λ. LD is a generalisation of the “polar” case for k = 1, and was originally conceived for a quite different purpose, viz. completeness of eigenfunctions via elliptic partial differential equation theory.

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