Journal ArticleDOI
Sturm-Liouville eigenvalue problems on time scales
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TLDR
For Sturm-Liouville eigenvalue problems on time scales with separated boundary conditions, an oscillation theorem is given and Rayleigh's principle is established, new in the discrete case.About:
This article is published in Applied Mathematics and Computation.The article was published on 1999-03-15. It has received 197 citations till now. The article focuses on the topics: Sturm–Liouville theory & Divide-and-conquer eigenvalue algorithm.read more
Citations
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Book
Dynamic Equations on Time Scales: An Introduction with Applications
Martin Bohner,Allan Peterson +1 more
TL;DR: The Time Scales Calculus as discussed by the authors is a generalization of the time-scales calculus with linear systems and higher-order linear equations, and it can be expressed in terms of linear Symplectic Dynamic Systems.
MonographDOI
Impulsive Differential Equations and Inclusions
TL;DR: Ben-chohra as discussed by the authors dedicates this book to his family members who complete us, and his children, Mohamed, Maroua, and Abdelillah; J. Henderson dedicates to his wife, Darlene and his descendants, Kathy.
Journal ArticleDOI
Dynamic equations on time scales: a survey
TL;DR: In this article, the authors give an introduction to the time scales calculus, and present various properties of the exponential function on an arbitrary time scale, and use it to solve linear dynamic equations of first order.
Journal ArticleDOI
On Green's functions and positive solutions for boundary value problems on time scales
TL;DR: In this article, a form of self-adjoint differential equations on time scales so that the associated Green's function is found symmetric in the usual sense is presented. And the concepts of Lebesgue delta and nabla integrals are introduced.
Book
Nonoscillation and Oscillation Theory for Functional Differential Equations
TL;DR: In this paper, the qualitative theory of differential equations with or without delays is summarized, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology.
References
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Journal ArticleDOI
Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus
Book
Difference Equations: An Introduction with Applications
Walter G. Kelley,Allan Peterson +1 more
TL;DR: The Difference Calculus of Variations as discussed by the authors is a generalization of the Difference calculus of Difference Equations (DCE) of the calculus of Variants (CDE) of Difference Functions.
Journal ArticleDOI
Basic Calculus on Time Scales and some of its Applications
Ravi P. Agarwal,Martin Bohner +1 more
TL;DR: In this article, the authors developed basic tools of calculus on time scales such as versions of Taylor's formula, l'Hospital's rule, and Kneser's theorem.
Book
Dynamic systems on measure chains
TL;DR: In this article, the authors present a technique for quantifying the stability of large-scale uncertain dynamic systems in terms of two measures, i.e., mean value theorem and Consequences.