Dynamic Equations on Time Scales: An Introduction with Applications

By Martin J. Bohner, Allan Peterson. 2001

3,152 citations recorded by the source corpus.

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Citations in the corpus

Oscillation Results for Second-order Linear Equations on a Time Scale (2002, background): “[2,9] for a discussion of rd-continuity, integration and other basic notions from the calculus on time scales.”
Higher-order self-adjoint boundary-value problems on time scales (2006, background): “Already several important problems concerning higher-order dynamic equations on time scales, involving only delta differentiation, have been developed [3,12–14,17,20,23,24].”
Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling (2008, background): “Created by Hilger in 1990 [23] and developed by others (see [5, 27] and references therein), this new and exciting type of mathematics is more general and versatile than the traditional theories of differential and difference equations as it can, under one framework, mathematically describe continuo”
Oscillation Criteria for Half-Linear Delay Dynamic Equations on Time Scales (2009, background): “Many other interesting time scales exist, and they give rise to many applications (see [3]).”
Hille and Nehari type criteria for third-order dynamic equations (2007, background): “The books on the subject of time scales by Bohner and Peterson [4] and [5] summarize and organize much of time scale calculus and some applications.”
Stability of abstract dynamic equations on time scales (2012, background): “For the theory of dynamic equations on time scales, we refer the reader to the very interesting monographs [2] and [3].”
Impulsive differential equations and inclusions (2006, background): “The time scales calculus has a tremendous potential for applications in some mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, social sciences, as is pointed out in the monographs of Aulbach”
Oscillation criteria for nonlinear functional neutral dynamic equations on time scales (2009, methodology): “[6] L. Erbe, T.S. Hassan, A. Peterson, and S.H. Saker, Oscillation criteria for sublinear half-linear delay dynamic equations on time scales, Int.”
The H-Laplace and Q-Laplace Transforms (2010, methodology): “The theory of Laplace transforms on time scales, which is intended to unify and to generalize the continuous and discrete cases, was initiated by Hilger [12] and then developed by Peterson and the authors [4–6].”