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MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE


To learn more about AIP Conference Proceedings,

including the Conference Proceedings Series, please visit the webpage http://proceedings.aip.org/proceedings


Melville, New York, 2009AIP CONFERENCE PROCEEDINGS 1124

SPONSORING ORGANIZATIONSUniversity of Santiago de Compostela.University of Vigo Ministry of Science and Innovation Xunta de Galicia Consolider Project- Ingenio MATHEMATICA Spanish Society of Applied Mathematics Spanish Royal Society of Mathematics Caixa Galicia Foundation International Federation of Nonlinear Analysts

MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINEProceedings of the International Conference on Boundary Value Problems

Santiago de Compostela, Spain 16 – 19 September 2008

EDITORS

Alberto CabadaUniversity of Santiago de Compostela, Spain

Eduardo Liz University of Vigo, Spain

Juan J. NietoUniversity of Santiago de Compostela, Spain.

All papers have been peer reviewed.


EditorsAlberto Cabada Departamento de Análisis Matemático Facultad de Matemáticas Universidad de Santiago de Compostela 15782, Spain E-mail: [email protected]

Eduardo Liz Departamento de Matemática Aplicada IIE.T.S. I. Telecomunicación Universidad de Vigo 36310, Spain E-mail: [email protected]

Juan J. Nieto Departamento de Análisis Matemático Facultad de Matemáticas Universidad de Santiago de Compostela 15782, Spain E-mail: [email protected]

L.C. Catalog Card No. 2009925594

ISBN 978-0-7354-0660-5ISSN 0094-243X

Printed in the United States of America

The articles on pp. 13 - 18 and 166 - 174 were authored by U.S. government employ-ees and are not covered under the below mentioned copyright.

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© 2009 American Institute of Physics

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CONTENTS

Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixCommittees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xSponsors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

CONTRIBUTIONS

Populational Growth Models Proportional to Beta Densities withAllee Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

S. M. Aleixo, J. L. Rocha, and D. D. PestanaImproved Predictor Corrector Method for Solving Fuzzy Initial ValueProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

T. Allahviranloo, N. Ahmady, and E. AhmadyA Note about Norbert Wiener and His Contribution to HarmonicAnalysis and Tauberian Theorems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

J. M. Almira and A. E. RomeroBound Sets Approach to BVPs: Retrospective and Perspectives. . . . . . . . . . . . . . . 29

J. AndresExistence of Solutions for Fourth-order ODE’s in Water Wave Models . . . . . . . . 39

M. O. Aprahamian and S. A. TersianRadial Solutions for Systems Involving Mean Curvature Operators inEuclidean and Minkowski Spaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

C. Bereanu, P. Jebelean, and J. MawhinLimit Cycles of Generalized Lienard Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Y. Bouattia and A. MakhloufPerturbations of a Spatial Ricker Model: Break of Chaos. . . . . . . . . . . . . . . . . . . . 71

E. Braverman and J. HaroutunianMathematical Model of Cancer with Competition. . . . . . . . . . . . . . . . . . . . . . . . . . . 79

J. M. Chrobak and H. HerreroMaximum Principles and Boundary Value Problems for FDEs. . . . . . . . . . . . . . . . 89

A. DomoshnitskyPositive Solutions for Boundary Value Problems of NonlinearFractional Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

M. El-ShahedPermanence for Multi-species Nonautonomous Lotka-VolterraCooperative Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Y. EnatsuA Second Order Non-autonomous Problem on the Half-line: AVariational Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

R. Enguica and L. SanchezSolvability of a Stationary Nonlinear Black-Scholes Equation underConditions on the Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

F. Fabiao, M. do Rosa´rio Grossinho and O. Simo˜es

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Global Stability and Singularities for Lotka-Volterra Systems withDelays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

T. FariaViability Theory Applied to Discontinuous Ordinary DifferentialEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

R. F. Sestelo and R. Lo´pez PousoMultiphase Systems for Medical Image Region Classification. . . . . . . . . . . . . . . . 158

J. F. Garamendi, N. Malpica and E. SchiaviAsymptotic Analysis in the Prandtl’ Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

D. V. GeorgievskiiNumerical Integration of Nonlinear Boundary Value Problems Arisingin Nucleation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

J. C. Gran˜a and I. E. ParraTwo-parameter Nonlinear Eigenvalue Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . 185

A. Gritsans, F. Sadyrbaev, and N. SergejevaHigher Order Nonlinear Two-point Boundary Value Problems withSign-type Nagumo Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

M. do Rosa´rio Grossinho, F. Minho´s, and A. I. SantosNonlocal Impulsive Boundary Value Problems with Solutions thatChange Sign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

G. Infante and P. PietramalaNumerical Methods for Singular Boundary Value Problems Involvingthe p-Laplacian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

P. Lima and L. MorgadoA Survey on the Limit Cycles of the Generalized Polynomial LienardDifferential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

J. LlibreSolutions of the Fully Fuzzy Linear System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

N. Mikaeilvand and T. AllahviranlooLocation Results: An Under Used Tool in Higher Order BoundaryValue Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

F. MinhosContractivity for Nonautonomous Logistic Equation with PiecewiseConstant Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

Y. Nakata, M. Kuroda, and Y. MuroyaExistence and Uniqueness Results for Fuzzy Differential EquationsSubject to Boundary Value Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

J. J. Nieto and R. Rodrı´guez-LopezOn Constant Sign Solutions„Nonpositive…of Certain FunctionalDifferential Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

Z. OplustilComponentwise Compression-expansion Conditions for Systems ofNonlinear Operator Equations and Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . 284

R. PrecupSingular Nonlinear Problem for Ordinary Differential Equation of theSecond-order on the Half- line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

I. Rachunkovaand J. Tomecˇek

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Exact and Approximate Solutions of Reaction-Diffusion-ConvectionEquations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

E. M. Rocha and M. M. Rodrigues

Mathematical Modeling of Neural Correlates of Cognition: The Caseof Selective Attention and Habituation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314

C. Trenado, L. Haab, and D. J. Strauss

On Solvability of a Three-point Boundary Value Problem for SecondOrder Nonlinear Functional Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . 322

P. Vodstrcil

Higher Order Non-local „n-1,1…Conjugate Type Boundary ValueProblems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

J. R. L. Webb

Analytic Normalizations of Analytic Integrable Systems . . . . . . . . . . . . . . . . . . . . 342X. Zhang

List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349Photograph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

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PREFACE

This volume consists of the Proceedings of the Conference on Boundary ValueProblems: Mathematical Models in Engineering, Biology and Medicine heldin Santiago de Compostela, Spain, from September 16 to September 19, 2008.The conference was intended to convene researchers and PhD students, toexchange ideas and discuss the trends and advances in the qualitative the-ory and applications of Differential Equations and Dynamical Systems in abroad sense. Many of the sessions were focused in Boundary Value Problems,but also other topics as stability theory, bifurcation, limit cycles, and globaldynamics were treated. A special emphasis was put in the applications in dif-ferent areas as population dynamics, models of tumor growth, digital imagesand neural networks. The papers collected in this volume are a good sam-ple of the several topics covered in the conference. They have been revisedthrough a rigorous refereing process, and they are presented in alphabeticalorder.

The Conference was attended by more than 120 researchers from morethan 20 different countries, and the scientific program combined plenary andinvited lectures, given by highly reputed experts, with contributed talks, allregarding the state of the art of theory and applications.

We would like to express our gratitude to all the speakers and partic-ipants, who made possible a very stimulating and scientifically interestingconference, with a friendly atmosphere.Santiago de Compostela, February 2009.

The Editors:Alberto CabadaEduardo LizJuan J. Nieto.

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CONFERENCE ON BOUNDARY VALUE PROBLEMS.

MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE

September, 16-19, 2008, Santiago de Compostela, Spain.

LOCAL ORGANIZING COMMITTEE

• Juan J. Nieto (Universidade de Santiago de Compostela, Spain) (Chairman) • Alberto Cabada (Universidade de Santiago de Compostela, Spain) (Vice-

chairman) • Eduardo Liz (Universidade de Vigo, Spain) (Coordinator) • Ignacio Bajo (Universidade de Vigo, Spain) • José A. Cid (Universidad de Jaén, Spain) • Juan B. Ferreiro (Universidade de Santiago de Compostela, Spain) • Daniel Franco (Universidad Nacional de Educación a Distancia, Spain), • Victoria Otero Espinar (Universidade de Santiago de Compostela, Spain) • Rodrigo López Pouso (Universidade de Santiago de Compostela, Spain) • Gerardo Rodríguez López (Universidade de Santiago de Compostela, Spain) • Rosana Rodríguez López (Universidade de Santiago de Compostela)

SCIENTIFIC COMMITTEE

• Ravi P. Agarwal (Florida Institute of Technology, U.S.A.) • Lansun Chen (Sinica Academy, P.R. China) • Pavel Drábek (University of West Bohemia, Czech Republic) • V. Lakshmikantham (Florida Institute of Technology, U.S.A.) • K. Gopalsamy (Flinders University of South Australia, Australia) • Jaume Llibre (Universitat Autònoma de Barcelona, Spain) • Jean Mawhin (Universitée Catholique de Louvain la Neuve, Belgium) • Donal O'Regan (National University of Ireland, Ireland) • Rafael Ortega (Universidad de Granada, Spain) • Jeff R. L. Webb (University of Glasgow, United Kingdom)

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SPONSORS

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ACKNOWLEDGMENTS

We are grateful to the Faculty of Mathematics of the University of Santiagode Compostela, where this Conference was held.

The conference was supported in part by the Spanish Ministry of Scienceand Innovation and FEDER, under grants MTM2007-61724 and MTM2007-60679, and under project Ingenio Mathematica (i-MATH), CSD2006-00032(Consolider–Ingenio 2010).

Financial support of the Galician Government under grants 2007/092 andPGIDIT06PXIB207023PR are gratefully acknowledged.

We give special thanks to the members of the Scientific Committee, andthe plenary lecturers, Professors Ravi P. Agarwal, Pavel Drabek, Jaume Lli-bre and Jean Mawhin.

We appreciate very much the professional job made by the members ofthe Organizing Committee, and the assistance of Beatriz Maquez both in thesecretary of the conference and in the edition of the book of proceedings.

Santiago de Compostela, February 2009.

The Editors:Alberto CabadaEduardo LizJuan J. Nieto.

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