Publication details

Eigenvalue and oscillation theorems for time scale symplectic systems



Year of publication 2011
Type Article in Periodical
Magazine / Source International Journal of Dynamical Systems and Differential Equations
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Time scale; Time scale symplectic system; Linear Hamiltonian system; Discrete symplectic system; Finite eigenvalue; Proper focal point; Generalized focal point; Oscillation theorem; Conjoined basis; Controllability; Normality; Quadratic functional
Attached files
Description In this paper we study eigenvalue and oscillation properties of time scale symplectic systems with Dirichlet boundary conditions. The focus is on deriving the so-called oscillation theorems for these systems, which relate the number of finite eigenvalues of the system with the number of proper (or generalized) focal points of the principal solution of the system. This amounts to defining and developing the central notions of finite eigenvalues and proper focal points for the time scale environment. We establish the traditional geometric properties of finite eigenvalues and eigenfunctions enjoyed by self-adjoint linear systems. We assume no controllability or normality of the system.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info