Asymptotic solution of eigenvalue problems for second-order ordinary differential equations

1975 ◽  
Vol 28 (6) ◽  
pp. 753-763 ◽  
Author(s):  
Donatus U. Anyanwu ◽  
Joseph B. Keller
Keyword(s):  
Differential Equations ◽  
Asymptotic Solution ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Second Order

The interlacing of eigenvalues for periodic multi-parameter problems

1978 ◽  
Vol 80 (3-4) ◽  
pp. 357-362 ◽  
Author(s):  
Patrick J. Browne
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Image Position ◽  
Periodic Equation

SynopsisThis paper studies a linked system of second order ordinary differential equationswhere xx ∈ [ar, br] and the coefficients qrars are continuous, real valued and periodic of period (br − ar), 1 ≤ r,s ≤ k. We assume the definiteness condition det{ars(xr)} > 0 and 2k possible multiparameter eigenvalue problems are then formulated according as periodic or semi-periodic boundary conditions are imposed on each of the equations of (*). The main result describes the interlacing of the 2k possible sets of eigentuples thus extending to the multiparameter case the well known theorem concerning 1-parameter periodic equation.

scholarly journals Solving Nonlinear Second Order Delay Eigenvalue Problems by Least Square Method

2020 ◽  
Vol 33 (4) ◽  
pp. 59
Author(s):  
Israa M. Salman ◽  
Eman A. Abdul-Razzaq
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Nonlinear Delay

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

Quadratic forms, weighted eigenfunctions and boundary value problems for non-linear second order ordinary differential equations

1989 ◽  
Vol 112 (1-2) ◽  
pp. 145-153 ◽  
Author(s):  
Alessandro Fonda ◽  
Jean Mawhin
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Quadratic Forms ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Second Order ◽  
Non Linear

SynopsisSome known results for different kinds of boundary value problems for second order ordinary differential equations are generalised. Different approaches are compared with one another, using topological and variational methods and the theory of weighted eigenvalue problems.

The Geometry of d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t), and Euclidean Spaces

2006 ◽  
Vol 49 (2) ◽  
pp. 170-184
Author(s):  
Richard Atkins
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Shortest Paths ◽  
Equivalence Problem ◽  
Second Order ◽  
System Of Differential Equations ◽  
Lagrange Equations ◽  
Invariant Functions ◽  
Underlying Geometry ◽  
The Relationship

AbstractThis paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are defined as the solutions to a pair of second-order differential equations: the Euler–Lagrange equations of the metric. We ask when the converse holds, that is, when solutions to a system of differential equations reveals an underlying geometry. Specifically, when may the solutions to a given pair of second order ordinary differential equations d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t) be reparameterized by t → T(y, t) so as to give locally the geodesics of a Euclidean space? Our approach is based upon Cartan's method of equivalence. In the second part of the paper, the equivalence problem is solved for a generic pair of second order ordinary differential equations of the above form revealing the existence of 24 invariant functions.

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