Functional Differential Equations and Applications

This book discusses delay and integro-differential equations from the point of view of the theory of functional differential equations. This book is a collection of selected papers presented at the international conference of Functional Differential Equations and Applications (FDEA-2019), 7th in the series, held at Ariel University, Israel, from August 22-27, 2019. Topics covered in the book include classical properties of functional differential equations as oscillation/non-oscillation, representation of solutions, sign properties of Green's matrices, comparison of solutions, stability, control, analysis of boundary value problems, and applications. The primary audience for this book includes specialists on ordinary, partial and functional differential equations, engineers and doctors dealing with modeling, and researchers in areas of mathematics and engineering.

Autorentext

Alexander Domoshnitsky is Full Professor at the Department of Mathematics and Computer Sciences, Ariel University, Israel, since 2009. Earlier, he was Dean of the Natural Science Faculty at Ariel University, Israel, from 20082015. He also was Senior Lecturer and Dozent (Associated Professor) at Perm Polytechnic Institute, Perm, Russia, from 19841990. Then he was Senior Lecturer and Associate Professor at the Department of Mathematics and Computer Sciences, Ariel University Center of Samaria, Ariel, Israel, from 19982009. He completed his Ph.D. in Mathematics from Tbilisi State University, Tbilisi, Russia, in 1984, and M.Sc. in Mathematics from Perm State University, Russia, in 1979. His areas of research include non-oscillation, maximum principle, boundary value problems for functional differential equations, theory of functional, stability of integro-differential equations, and theory of impulsive differential equations. He has visited institutions and universities around the globe to deliver invited talks and lectures. Seven students have completed their Ph.D. under his direct supervision. He is Co-author of Nonoscillation Theory of Functional Differential Equations with Applications (Springer, 2012) and Oscillation, Stability and Asymptotic Properties for second and Higher Order Functional Differential Equations. With over 140 research articles published in international journals and conference proceedings of repute, he is on the editorial board of several mathematics journals and Editor-in-Chief of the Functional Differential Equations journal being published by Ariel University since 1993.

Alexander Rasin is Lecturer at the Department of Mathematics, Ariel University, Israel. Earlier, he held postdoctoral positions at Bar-Ilan University and Weizmann Institute of Science, Israel. Later, he joined the Department of Mathematics and Computer Science at Ariel University, Israel. He received his Ph.D. from the University of Surrey, Guildford, UK, and master's degree from the Dnepropetrovsk National University, Ukraine. His research includes exactly solvable and integrable systems, symmetries for partial and difference equations, and exploring solutions for the wave equations. Alexander is Associate Editor of the Functional Differential Equations journal. His research articles have been published in several national and international journals of repute.

Seshadev Padhi is Professor of Mathematics at the Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi, India. He received the BOYSCAST award in 2004 from the Department of Science and Technology, the Government of India. He earlier worked at the Department of Mathematics and Statistics, Mississippi State University, USA. His areas of research include non-oscillation, stability, and positive solutions to boundary value problems. Two students have completed their Ph.D. under the supervision of Prof. Padhi. With over 100 research papers published in several international journals of repute, he is Active Reviewer for the Mathematical Review and Zentralblatt Math as well as several international journals of repute. He has co-authored two research monographs: Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics (Springer, 2014) and Theory of Third-Order Differential Equations (Springer, 2013).

Inhalt
Angela Slavova: Dynamical Behaviour of Integro-Differential Equations arising in Nano-Structures.- Jiri Benedikt, Petr Girg, and Lukas Kotrla: Nonlinear Models of the Fluid Flow in Porous Media and Their Methods of StudyMikhail Chirkov and S.Sergey Rusakov: Modeling of Control of the Immune Response in the Acute Form of an Infectious Disease under Conditions of Uncertainty.- G.V. Demidenko and I.I. Matveeva: The Second Lyapunov Method for Time-Delay Systems.- S.V. Rusakov, V.G. Gilev, and A.Yu. Rakhmanov: Diffusion-Kinetic Model of Curing of Epoxy Polymer.- Vasyl Martsenyuk, Mikolaj Karpinski, Aleksandra Klos-Witkowska, and Andriy Sverstiuk: On Qualitative Research of Lattice Dynamical System of Two- and Three-Dimensional Biopixels Array.- Khusainov Denys and Bychkov Oleksii: Research on Solutions Stability for Dynamic Switched Time-Delay Systems.- Gershon Kresin and Tehiya Ben Yaakov: Some Extremal Problems for Solutions of the Modified Helmholtz Equation in the Half-Space.- Medea Iordanishvili, Tea Shavadze and Tamaz Tadumadze: Delay Optimization Problem for One Class of Functional Differential Equation.- Alexey Kolchev and Ivan Egoshin: Some Problems of Mathematical Modeling of Radiophysical Sounding Signals.- Roman Koplatadze and Ivan Egoshin: Oscillation Criteria for Higher-Order Linear Differential Equations.- Irina Astashova, Alexey Filinovskiy and Dmitriy: On Necessary Conditions of Optimality to the Extremal Problem for Parabolic Equations.- T. Lazebnik, S. Yanetz, and S. Bunimovich-Mendrazitsky: PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy.- A.V. Podolskiy and T.A. Shaposhnikova: Homogenization of a Parabolic Equation for P-Laplace Operator in a Domain Perforated along (N 1)-Dimensional Manifold with Dynamical Boundary Condition Specified On Perforations Boundary: Critical Case.- Seshadev Padhi: Positive Solutions of Cantilever Beam Equation Depending on Parameter.- Irina Volinsky, Alexander Domoshnitsky, Marina Bershadsky and Roman Shklyar: Marchuk's Models of Infection Diseases: New Developments.- Yaroslav Petrivskyi and Volodymyr Petrivskyi: Some Properties of the Solution of the Nonlinear Equation of Oscillations in Modeling the Magnetic Separation.- Sergey Labovskiy and Manuel Alves: Poisson Problem for a Functional Differential Equation: Positivity of a Quadratic Functional, Jacobi Condition.- Tatiana Korchemkina: On Asymptotic Behavior of the First Derivatives of Bounded Solutions to Second-Order Differential Equations with General Power-Law Nonlinearity.- Alexander Domoshnitsky, Oleg Kupervasser, Hennadii Kutomanov, and Roman Yavich: A Method for Stabilization of Ground Robot Path Controlled by Airborne Autopilot with Time Delay.- Dan Gamliel: Periodic Solutions for a Class of Impulsive Delay Differential Equations.