International Journal of Differential Equations

/ / Special Issue

Recent Advances in Oscillation Theory

Publishing date

01 May 2010

Status

Published

Submission deadline

01 Nov 2009

Lead Editor

Yuriy Rogovchenko

Guest Editors

Leonid Berezansky¹ | Elena Braverman² | Josef Diblík

¹Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

²Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary AB, Canada T2N 1N4

Recent Advances in Oscillation Theory

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Description

The theory of oscillations is an important branch of the applied theory of differential equations related to the study of oscillatory phenomena in technology, as well as natural and social sciences. Fundamental problems of the classical theory of oscillations consist in proving the existence or nonexistence of oscillatory (periodic, almost-periodic, etc.) solutions of a given equation or system, and, in simpler cases, funding such solutions. Furthermore, the behavior of other solutions in relation to a given oscillatory (nonoscillatory) solution is often investigated.

Every year hundreds of papers on theoretical aspects of oscillations of solutions to various classes of equations, including ordinary and functional differential equations as well as difference, dynamic, and partial differential equations, are published. However, this important branch of research is not purely theoretical and has very important applications. For instance, recent studies suggest that many animal and plant populations oscillate in synchrony because of the interactions such as predation and competition. Coupled oscillating biological populations can give rise to potentially important effects such as “synchronized chaos.” Therefore, through the study of oscillations, one gets deeper insights into the behavior of complex biological and social systems.

We invite researchers to present original articles that address new challenging problems related to linear and nonlinear oscillations or describe novel techniques and approaches to classical problems in the theory of oscillation, as well as survey papers illuminating important recent developments and contributing to further progress in this important branch of the qualitative theory of differential equations. We particularly welcome manuscripts dealing with oscillation or nonoscillation of solutions in applied problems arising in engineering, technology, natural, and social sciences. The topics to be covered include, but are not limited to:

Oscillation in ordinary differential equations
Oscillation in functional differential equations
Oscillation in difference equations
Oscillation in dynamic equations
Oscillation in equations on time scales
Oscillation in systems of differential and functional-differential equations
Oscillation in impulsive differential equations
Oscillation in matrix equations
Oscillation in partial differential equations
Control and stabilization of oscillations
Synchronization of oscillations
Oscillations in biological, mechanical systems

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/ijde/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/ according to the following timetable: