editorial functional differential and difference equations with...
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EditorialFunctional Differential and Difference Equations withApplications 2013
J. Diblík,1 E. Braverman,2 I. Györi,3 Yu. Rogovchenko,4 M. RRDiIková,5 and A. Zafer6
1 Brno University of Technology, Brno, Czech Republic2 University of Calgary, Calgary, Canada3University of Pannonia, Veszprém, Hungary4University of Agder, Kristiansand, Norway5University of Žilina, Žilina, Slovakia6Middle East Technical University, Ankara, Turkey
Correspondence should be addressed to J. Dibĺık; [email protected]
Received 27 January 2014; Accepted 27 January 2014; Published 12 May 2014
Copyright © 2014 J. Dibĺık et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This annual issue comes as a sequel to two special issues,Recent Progress in Differential andDifference Equations editedby the four members of the present team and FunctionalDifferential and Difference Equations with Applications withthe same editorial team, both published by the Abstract andApplied Analysis in 2011 and 2012, respectively.
In the call for papers prepared by the Guest Editors andposted on the journal’s web page, we encouraged submissionof state-of-the-art contributions on a wide spectrum of topicssuch as asymptotic behavior of solutions, boundedness andperiodicity of solutions, nonoscillation and oscillation ofsolutions, representation of solutions, stability, numericalalgorithms, and computational aspects, as well as applica-tions to real-world phenomena. This invitation was warmlywelcomed by the mathematical community; more than sixtymanuscripts addressing important problems in the above-mentioned fields of qualitative theory of functional differen-tial and difference equations were submitted to the EditorialOffice and went through a thorough peer refereeing process.Twenty-seven carefully selected research articles collectedin this special issue reflect modern trends and advances infunctional differential and difference equations. Sixty-sevenauthors from fourteen countries (China, Czech Republic,Georgia, Hungary, Israel, Latvia, Norway, Portugal, SaudiArabia, Serbia, Slovak Republic, Spain, Turkey, and Ukraine)have contributed to the success of this thematic collection ofpapers.
Questions related to the existence of periodic solutionsand their stability properties traditionally attract attentionof researchers working in the qualitative theory of differen-tial, functional differential, and difference equations. In thisissue, the reader will find results that relate periodicity oflinear autonomous nonhomogeneous difference equations tothe existence of equilibria. Systems of nonlinear differenceequations whose all well-defined solutions are periodic areconsidered. For some classes of nonlinear systems with delay,it is shown that the presence of the time delay results in theexistence of periodic solutions.
Existence of oscillating solutions for half-linear differen-tial equations with delay and for even order damped equa-tions with distributed deviating arguments is studied. Non-linear oscillations in the context of saddle-center bifurcationin the dynamical system describing a singularly perturbedforced oscillator of Duffing’s type with a nonlinear restoringand a nonperiodic external driving force are examined.Boundedness of solutions to a class of second-order periodicsystems with singularities is considered as well.
Stability problems always attract interest of researchers,and this special issue is not an exception. The reader willfind papers on the stability of impulsive stochastic functionaldifferential equations with delayed impulses and stabilityof differential systems under permanently arising impulses,an application of moment equations in a model of thestable foreign currency exchange market in conditions of
Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014, Article ID 543797, 2 pageshttp://dx.doi.org/10.1155/2014/543797
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2 Abstract and Applied Analysis
uncertainty, a study on the global exponential stability ofequilibria for impulsive cellular neural network models withpiecewise alternately advanced and retarded arguments, andanalysis of stability and global Hopf bifurcation phenomenain a ratio-dependent predator-prey model with two timedelays.
New results for boundary value problems are alsoreported, including the existence and uniqueness theoremfor solutions of nonhomogeneous impulsive boundary valueproblem for planar Hamiltonian systems and general resultson the solvability of singular initial value problems.
Several articles deal with the behavior of solutions atinfinity. Namely, explicit formulas for planar weakly delayedlinear discrete systems are derived; results on asymptoticbehavior of solutions to generalized Emden-Fowler differen-tial equations with delayed argument, higher-order quasilin-ear neutral differential equations, vector integral equationswith deviating arguments, and linear Volterra integrodif-ferential systems are reported along with the applicationsof nonlinear weakly singular inequalities to Volterra-typedifference equations.
Other important problems discussed in this special issueare related to the representation of the solutions of lineardiscrete systems with constant coefficients and two delays,automorphisms of ordinary differential equations, spatialdiscretization of the Cauchy problem for a multidimensionallinear parabolic partial differential equation of the secondorder with nondivergent operator, and unbounded time-and space-dependent coefficients. Newton-Kantorovich andSmale type convergence theorems are used in a deformedNewton method with the third-order convergence for solv-ing nonlinear equations. Regularity of a mild solution fora stochastic fractional delayed reaction-diffusion equationdriven by Lévy space-time white noise and an inverseproblem for Dirac differential operators with discontinu-ity conditions and discontinuous coefficient are studied.Finally, a mathematical model for the incompressible two-dimensional/axisymmetric non-Newtonian fluid flows andheat transfer analysis in the region of stagnation point over astretching/shrinking sheet and axisymmetric shrinking sheetis presented.
It is not possible to provide in this short editorial note adetailed description for all papers included in this volume.However, it is clear that they reflect contemporary trendsin the development of the qualitative theory of functionaldifferential equations and feature important applications. Webelieve that this special issue challenges researchers withnew unsolved problems and introduces many new ideas anduseful techniques.
J. DibĺıkE. Braverman
I. GyöriYu. Rogovchenko
M. RůžičkováA. Zafer
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