Online citations, reference lists, and bibliographies.

Basic Calculus On Time Scales And Some Of Its Applications

R. Agarwal, M. Bohner
Published 1999 · Mathematics

Cite This
Download PDF
Analyze on Scholarcy
Share
The study of dynamic systems on time scales not only unifies continuous and discrete processes, but also helps in revealing diversities in the corresponding results. In this paper we shall develop basic tools of calculus on time scales such as versions of Taylor’s formula, l’Hôspital’s rule, and Kneser’s theorem. Applications of these results in the study of asymptotic and oscillatory behavior of solutions of higher order equations on time scales are addressed. As a further application of Taylor’s formula, Abel-Gontscharoff interpolating polynomial on time scales is constructed and best possible error bounds are offered. We have also included notes at the end of each section which indicate further scope of the calculus developed in this paper.
This paper references



This paper is referenced by
OSCILLATION THEORY FOR SECOND ORDER DIFFERENTIAL EQUATIONS AND DYNAMIC EQUATIONS ON TIME SCALES
Ahmet Yantir (2004)
10.1137/1.9781611973273.14
Periodic Control System Stabilization on Time Scales
F. Miranda (2013)
10.1080/1026190290017360
Perturbations of Dynamic Equations
M. Bohner (2002)
10.1016/j.mcm.2006.03.021
Multiple positive solutions for the one-dimensional p-Laplacian dynamic equations on time scales
Z. He (2007)
10.4064/SM162-2-4
Vitali Lemma approach to differentiation on a time scale
C. J. Chyan (2004)
10.1016/S0377-0427(99)00267-8
Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain
L. Erbe (2000)
10.1016/J.CNSNS.2010.06.029
Existence of quasibounded solutions for the higher order dynamic equations on measure chains
Haihui Wu (2011)
10.1186/S13662-015-0428-4
Positive solutions to PBVPs for nonlinear first-order impulsive dynamic equations on time scales
Wen Guan (2015)
10.1155/2016/7327319
On Some Existence and Uniqueness Results for a Class of Equations of Order on Arbitrary Time Scales
Abdourazek Souahi (2016)
Dynamic equations (…) on time scales
A. Sikorska-Nowak (2011)
10.1080/1026190290017405
Double Solutions of Impulsive Dynamic Boundary Value Problems on a Time Scale
J. Henderson (2002)
10.1155/2008/576876
Diamond- Jensen's Inequality on Time Scales
M. R. Sidi Ammi (2007)
10.1080/10236190290017450
Eigenvalue Intervals for 2mth Order Sturm—Liouville Boundary Value Problems
C. J. Chyan (2002)
Opial's Inequality on Time Scales and an Application
T. Gray (2007)
Ostrowski Type Inequalities on Time Scales
C. Dinu (2007)
Zaman Skalasinda Box-Cox Regresyon Yöntemi
Mayneur Niyazi (2012)
10.3968/J.PAM.1925252820120402.1785
Nonoscillation for System of Neutral Delay Dynamic Equation on Time Scales
Guohua Liu (2012)
10.14403/JCMS.2014.27.4.661
THE Mα-DELTA INTEGRAL ON TIME SCALES
Jae Myung Park (2014)
10.14403/JCMS.2013.26.2.435
THE HESTOCK AND HENSTOCK DELTA INTEGRALS
Jae Myung Park (2013)
10.1109/chicc.2016.7553298
Exponential stability of non-autonomous systems with time delay on time scales
Lu Xiaodong (2016)
10.1155/2009/496135
Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales
Chao Zhang (2009)
10.14403/JCMS.2014.27.2.327
THE RIEMANN DELTA INTEGRAL ON TIME SCALES
Jae Myung Park (2014)
10.1007/978-3-030-15420-2_9
Oscillations of Second-Order Nonlinear Functional Dynamic Equations
Svetlin Georgiev Georgiev (2019)
10.7153/MIA-17-35
Higher order dynamic inequalities on time scales
S. H. Saker (2014)
10.1134/S0001434619010139
Extremal Solutions for Nonlinear First-Order Impulsive Integro-Differential Dynamic Equations
L. Zhang (2019)
10.1016/J.CAMWA.2004.07.012
Constant-sign solutions for a system of integral equations on time scales
P. J. Y. Wong (2005)
10.1007/S10440-008-9294-3
Multiple positive solutions for time scale boundary value problems on infinite intervals
X. Zhao (2008)
10.1080/00036811.2013.867019
Floquet theory for a Volterra integro-dynamic system
R. Agarwal (2014)
General Cauchy-Lipschitz theory for shifted and non shifted ∆-Cauchy problems on time scales
Löıc Bourdin (2012)
10.1155/2019/4748373
A Note on Integral Inequalities on Time Scales Associated with Ostrowski’s Type
Saeeda Fatima Tahir (2019)
Positive Solutions for Eigenvalue Problem with Time Scales
Hu Liang-gen (2009)
10.1155/2010/620459
Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales
Ya-Hong Zhao (2010)
See more
Semantic Scholar Logo Some data provided by SemanticScholar