On Boundary Value Problems for Hamiltonian Systems with Two Singular Points

1984 ◽  
Vol 15 (2) ◽  
pp. 272-286 ◽  
Author(s):  
D. B. Hinton ◽  
J. K. Shaw
Keyword(s):  
Boundary Value Problems ◽  
Hamiltonian Systems ◽  
Boundary Value ◽  
Singular Points

Finding singular points of two-point boundary value problems

1986 ◽  
Vol 65 (1) ◽  
pp. 244-250 ◽  
Author(s):  
George Witmer ◽  
Vemuri Balakotaiah ◽  
Dan Luss
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Singular Points ◽  
Point Boundary

scholarly journals Stiff systems of ordinary differential equations

1981 ◽  
Vol 23 (2) ◽  
pp. 136-172 ◽  
Author(s):  
J. J. Mahony ◽  
J. J. Shepherd
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Singular Points ◽  
Operator Norm ◽  
Existence Theory ◽  
Stiff Systems ◽  
Stiff System ◽  
Linear Differential ◽  
Image Position

AbstractSolutions of the stiff system of linear differential equationsare obtained in a form yielding tight estimates of their properties, and conditions are obtained under which the operator norm of the map from r to the solution x does not become exponentially large for small values of ε. When these conditions are satisfied, the solutions are shown to be close to those of Ax + r = 0, save at any singular points of A, and in boundary layers. The behaviour of solutions near admissible singular points is also obtained.The results are used to characterize those boundary-value problems for the above system in which the solution defines maps from the data that are of “moderate” operator norm. This leads to a constructive existence theory for a limited class of boundary-value problems for the nonlinear systemIt is suggested that the treatment of more general classes of boundary-value problems may be simplified using these results. By the use of simple examples, the problems involving large operator norms are shown to be related to the stability properties of the possible branches of the outer solutions close to those of

scholarly journals Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Shurong Sun ◽  
Martin Bohner ◽  
Shaozhu Chen
Keyword(s):  
Boundary Value Problems ◽  
Spectral Theory ◽  
Hamiltonian Systems ◽  
Dynamic Systems ◽  
Time Scale ◽  
Boundary Value ◽  
Hamiltonian Dynamic ◽  
Special Cases ◽  
Linear Hamiltonian Systems ◽  
Singular Hamiltonian Systems

We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for𝕋=ℝand𝕋=ℤwithin one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i)M(λ)theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.

Sign in / Sign up

Export Citation Format

Share Document