In 1836-1837 Sturm and Liouville published a series of papers on second order linear
ordinary differential operators, which started the subject now known as the Sturm-Liouville …

Linear and nonlinear Hamiltonian systems are studied on time scales T. We unify symplectic
flow properties of discrete and continuous Hamiltonian systems. A chain rule which unifies …

The book presents a systematic and compact treatment of the qualitative theory of half-linear
differential equations. It contains the most updated and comprehensive material and …

Half-linear differential equations Page 172 CHAPTER 3 Half-Linear Differential Equations O.
Došlý Masaryk University, Department of Mathematics, Janackovo nam. 2A, 662 95 Brno …

In this paper we prove various optimal bounds for eigenvalue ratios for the Sturm-Liouville
equation−[p (x) y′]′+ q (x) y= λw (x) y and certain specializations. Our results primarily …

We examine how Sturm's oscillation theorems on comparison, separation, and indexing the
number of zeros of eigenfunctions have evolved. It was Bôcher who first put the proofs on a …

In this paper we study qualitative properties of the socalled symplectic dynamic system (S)
zδA= Stz on an arbitrary time scale T, providing a unified theory for discrete symplectic …

Presenting the proceedings of the conference on Sturm-Liouville problems held in
conjunction with the 26th Barrett Memorial Lecture Series at the University of Tennessee …

1. Introduction. Let P (x) be an m× m matrix-valued function that is continuous, real,
symmetric, and positive definite for all x in an interval J, which will be further specified. Let w …

In this paper we derive a general limit characterization of principal solutions at infinity of
linear Hamiltonian systems under no controllability assumption. The main result is …