DOUBLY PERIODIC FLOQUET THEORY FOR A SECOND ORDER SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS

1986 ◽  
Vol 37 (3) ◽  
pp. 347-356 ◽  
Author(s):  
B. D. SLEEMAN ◽  
P. D. SMITH
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Floquet Theory ◽  
Second Order ◽  
Order System

Periodic Solutions of Systems with Singularities of Repulsive Type

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Pablo Amster ◽  
Manuel Maurette
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Topological Degree ◽  
Second Order ◽  
Order System ◽  
Motion Model ◽  
Topological Degree Methods ◽  
Central Motion

AbstractMotivated by the classical Coulomb central motion model, we study the existence of T-periodic solutions for the nonlinear second order system of singular ordinary differential equations u′′ + g(u) = p(t). Using topological degree methods, we prove that when the nonlinearity g : ℝ

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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