Table Of ContentSpringer Proceedings in Mathematics & Statistics
Sandra Pinelas · Tomás Caraballo
Editors
Peter Kloeden · John R. Graef
Differential
and Difference
Equations with
Applications
ICDDEA, Amadora, Portugal, June 2017
Springer Proceedings in Mathematics & Statistics
Volume 230
Springer Proceedings in Mathematics & Statistics
This book series features volumes composed of selected contributions from
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á
Sandra Pinelas Tom s Caraballo
(cid:129)
Peter Kloeden John R. Graef
(cid:129)
Editors
Differential and Difference
Equations with Applications
ICDDEA, Amadora, Portugal, June 2017
123
Editors
Sandra Pinelas PeterKloeden
Departamento deCiências Centerfor Mathematical Sciences
ExactaseEngenharia HuazhongUniversity of Science
Academia Militar andTechnology
Amadora Wuhan, Hubei
Portugal China
TomásCaraballo JohnR. Graef
FacultaddeMatemáticas Department ofMathematics
Universidad deSevilla University of Tennessee at Chattanooga
Sevilla Chattanooga, TN
Spain USA
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-319-75646-2 ISBN978-3-319-75647-9 (eBook)
https://doi.org/10.1007/978-3-319-75647-9
LibraryofCongressControlNumber:2018932549
MathematicsSubjectClassification(2010): 34-XX,35-XX,37-XX,39-XX,45-XX
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Preface
Forthefivedays5–9June2017,morethan230mathematiciansfrom52countries
attended the 3rd International Conference on Differential & Difference Equations
and Applications, held at the Military Academy, Amadora, Portugal.
The scientific aim of this conference was to bring together mathematicians
working in various disciplines of differential and difference equations and their
applications. There were 12 plenary lectures, 14 main lectures and 175 commu-
nications about the current research in this field. This volume contains 50 selected
original papers which are connected to research lectures given at the conference.
Each paper has been carefully reviewed.
We take this opportunity to thank all the participants of the conference and the
contributors to these proceedings. Our special thanks belong to the Military
Academy for the sincere hospitality. We are also grateful to the Scientific and
Organizing Committees for all the effort in the preparation of the conference.
The conference was dedicated at memory of Prof. Ondřej Došlý (1956–2016).
ProfessorOndřejDošlýhadbeeninvitedtotheICDDEA2011asaplenaryspeaker,
to the ICDDEA 2015 as Scientific Committee and main speaker and to the
ICDDEA 2017 plenary speaker, but was unable to come and died shortly
afterwards.
We hope that this volume will serve researchers in all fields of differential and
difference equations.
Amadora, Portugal Sandra Pinelas
Sevilla, Spain Tomás Caraballo
Wuhan, China Peter Kloeden
Chattanooga, USA John R. Graef
v
Contents
On Asymptotic Behavior of Blow-Up Solutions to Higher-Order
Differential Equations with General Nonlinearity. . . . . . . . . . . . . . . . . . 1
Irina V. Astashova
Discrete Heat Equation with Shift Values . . . . . . . . . . . . . . . . . . . . . . . 13
G. Britto Antony Xavier, S. John Borg and M. Meganathan
A Note on the Existence for a Model of Turbulent Flows Through
Porous Media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Hermenegildo Borges de Oliveira
Critical Point Approaches to Difference Equations
of Kirchhoff-Type. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Shapour Heidarkhani, Ghasem A. Afrouzi, Shahin Moradi
and Giuseppe Caristi
Continuous Selections of Solution Sets of a Second-Order
Integro-Differential Inclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Aurelian Cernea
Factorization Method and General Second Order Linear Difference
Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Alina Dobrogowska and Mahouton Norbert Hounkonnou
Homogeneous Boundary Problem for the Compressible Viscous
and Heat-Conducting Micropolar Fluid Model with Cylindrical
Symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Ivan Dražić
Hermite–Fejer Polynomials as an Approximate Solution of Singular
Integro-Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Alexander Fedotov
vii
viii Contents
On Nonexistence of Solutions to Some Nonlinear Functional
Differential Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Evgeny Galakhov and Olga Salieva
The Common Descent of Biological Shape Description
and Special Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
J. Gielis, D. Caratelli, C. Moreno de Jong van Coevorden and P. E. Ricci
Variational Iteration Method for Solving Problems
with Integral Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Ahcene Merad and Samir Hadid
Kirchhoff-Type Boundary-Value Problems on the Real Line . . . . . . . . . 141
Shapour Heidarkhani, Amjad Salari and David Barilla
Comparison of Known Existence Results for One-Dimensional
Beam Models of Suspension Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Jakub Janoušek
A Certain Class of Harmonic Mappings Related to Functions
of Bounded Radius Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Yasemin Kahramaner, Yaşar Polatog̃lu and Arzu Yemişci Şen
Entropy of Nonautonomous Dynamical Systems . . . . . . . . . . . . . . . . . . 179
Christoph Kawan
A Proposal for an Application of a Max-Type Difference Equation
to Epilepsy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
David M. Chan, Candace M. Kent, Vlajko Kocić and Stevo Stević
On the Maximum Principle for Systems with Delays . . . . . . . . . . . . . . . 211
A. V. Kim, V. M. Kormyshev and A. V. Ivanov
Hyperbolicity and Solvability for Linear Systems on Time Scales . . . . . 221
Sergey Kryzhevich
Oscillation of Third-Order Nonlinear Neutral Differential
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Petr Liška
Conjecture on Fučík Curve Asymptotes for a Particular Discrete
Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Iveta Looseová
Interval Difference Methods for Solving the Poisson Equation. . . . . . . . 259
Andrzej Marciniak and Tomasz Hoffmann
Gevrey Well Posedness of Goursat-Darboux Problems and
Asymptotic Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Jorge Marques and Jaime Carvalho e Silva
Contents ix
Oscillation Criteria for a Difference System with Two Delays . . . . . . . . 285
Pati Doi and Hideaki Matsunaga
log0¼log1¼0 and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Hiroshi Michiwaki, Tsutomu Matuura and Saburou Saitoh
Collocation Method to Solve Second Order Cauchy
Integro-Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Abdelaziz Mennouni and Nedjem Eddine Ramdani
Approximative Solutions to Autonomous Difference Equations
of Neutral Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Janusz Migda
Asymptotic Properties of Nonoscillatory Solutions
of Third-Order Delay Difference Equations . . . . . . . . . . . . . . . . . . . . . . 327
Alina Gleska and Małgorzata Migda
On Copson’s Theorem and Its Generalizations . . . . . . . . . . . . . . . . . . . 339
A. Linero Bas and D. Nieves Roldán
Global Asymptotic Stability of a Non-linear Population
Model of Diabetes Mellitus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Silvia Rodrigues de Oliveira, Soumyendu Raha and Debnath Pal
On a Nonlocal Boundary Value Problem for First Order
Nonlinear Functional Differential Equations . . . . . . . . . . . . . . . . . . . . . 359
Zdeněk Opluštil
Existence Results for Fuzzy Differential Equations via Truncation
Operators Between an Upper and a Lower Solution and Fixed Point
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
Rosana Rodríguez-López
On Systems of Nonlinear ODE Arising in Gas Dynamics: Application
to Vortical Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
Olga S. Rozanova and Marko K. Turzynski
Division by Zero Calculus and Differential Equations . . . . . . . . . . . . . . 399
Sandra Pinelas and Saburou Saitoh
Optimality Conditions for Multidimensional Variational Problems
Involving the Caputo-Type Fractional Derivative. . . . . . . . . . . . . . . . . . 419
Barbara Łupińska, Tatiana Odzijewicz and Ewa Schmeidel
Maximum Principle for a Kind of Elliptic Systems
with Morrey Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
Lubomira G. Softova
x Contents
A Survey on the Oscillation of Delay Equations with A Monotone
or Non-monotone Argument. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
G. M. Moremedi and I. P. Stavroulakis
Discrete Versions of Some Dirac Type Equations
and Plane Wave Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
Volodymyr Sushch
Analytic Representation of Generalized Möbius-Listing’s Bodies
and Classification of Links Appearing After Their Cut . . . . . . . . . . . . . 477
Sandra Pinelas and Ilia Tavkhelidze
Existence and Multiplicity of Periodic Solutions
to Fractional p-Laplacian Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
Lin Li and Stepan Tersian
Oscillation of Third Order Mixed Type Neutral
Difference Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
S. Selvarangam, M. Madhan, E. Thandapani and S. Pinelas
The Fuzzy Henstock–Kurzweil Delta Integral on Time Scales . . . . . . . . 525
Dafang Zhao, Guoju Ye, Wei Liu and Delfim F. M. Torres
Oscillation of Sublinear Second Order Neutral Differential
Equations via Riccati Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . 543
Arun Kumar Tripathy and Abhay Kumar Sethi
Steady and Unsteady Navier–Stokes Flow with Lagrangian
Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
Werner Varnhorn
On Some Discrete Boundary Value Problems
in Canonical Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
Alexander V. Vasilyev and Vladimir B. Vasilyev
Asymptotic Behaviour in a Certain Nonlinearly Perturbed Heat
Equation: Non Periodic Perturbation Case . . . . . . . . . . . . . . . . . . . . . . 581
Carlos Ramos, Ana Santos and Sandra Vinagre
Mathematical Model for Optimising Bi-Enzyme Biosensors. . . . . . . . . . 595
Qi Wang and Yupeng Liu
Fibonacci Series with Several Parameters . . . . . . . . . . . . . . . . . . . . . . . 617
G. Britto Antony Xavier and B. Mohan
Comparison Theorems for Second-Order Damped Nonlinear
Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627
Naoto Yamaoka
