Integral and Integrodifferential Equations: Theory, Methods and Applications

340 Pages·2000·15.04 MB·English

by  Ravi P. Agarwal

INTEGRAL AND
INTEGRODIFFERENTIAL
EQUATIONS
Theory, Methods and
Applications
INTEGRAL AND INTEGRODIFFERENTIAL
EQUATIONS
SERIES IN MATHEMATICAL ANALYSIS AND APPLICATIONS
Series in Mathematical Analysis and Applications (SIMAA) is edited by Ravi P. Agarwal,
National University of Singapore and Donal O’Regan, National University of Ireland.
The series is aimed at reporting on new developments in mathematical analysis and
applications of a high standard and of current interest. Each volume in the series is devoted
to a topic in analysis that has been applied, or is potentially applicable, to the solutions
of scientific, engineering and social problems.
Volume 1
Method of Variation of Parameters for Dynamic Systems
V. Lakshmikantham and S.G. Deo
Volume 2
Integral and Integrodifferential Equations: Theory, Methods and Applications
edited by Ravi P. Agarwal and Donal O* Regan
This book is part of a series. The publisher will accept continuation orders which may be cancelled
at any time and which provide for automatic billing and shipping of each title in the series upon
publication. Please write for details.
INTEGRAL AND INTEGRODIFFERENTIAL
EQUATIONS
Theory, Methods and Applications
Edited by
Ravi P. Agarwal
National University of Singapore
and
Donal O’Regan
National University of Ireland
GORDON AND BREACH SCIENCE PUBLISHERS
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Copyright © 2000 OPA (Overseas Publishers Association) N. V. Published by license under
The Gordon and Breach Science Publishers imprint.
All rights reserved.
No part of this book may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and recording, or by any information storage or
retrieval system, without permission in writing from the publisher. Printed in Singapore.
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
ISBN: 90-5699-221-X
ISSN: 1028-8600
In memory of
Professor Günther Hämmerlin

Contents
Preface xi
1. The Solution Set of Integral Inclusions on the Half Line 1
R.P Agarwal and D. O’Regan
2. Periodic Solutions of Integrodifferential Inclusions 9
R.P Agarwal and D. O'Regan
3. On Nonlinear Volterra-Stieltjes Integral Operators 21
J. Banati
4. A Modified Collocation Method for Volterra Delay Integrodifferential
Equations with Multiple Delays 39
A. Burgstaller
5. On the Numerical Solution of Initial Boundary Value Problems by the
Laguerre Transformation and Boundary Integral Equations 55
R. Chapko and R. Kress
6. Remarks on Hammerstein Integral Operators 71
G. Emmanuele
7. Preserving Transient Behaviour in Numerical Solutions of Volterra
Integral Equations of Convolution Type 77
N.J. Ford and C.T.H. Baker
8. A Spline Method for the Numerical Solution of Volterra Integral Equations
of the Second Kind 91
L. Gori and E. Santi
vii
viii CONTENTS
9. Boundary Value Problems for a Class of Integro-differential Equations
and Applications 101
R.B. Guenther and J.W. Lee
10. Integro-Differential Equations on Unbounded Domains in Banach Spaces 117
D. Guo
11. Global Attractivity in Diffusive Integrodifferential Equations 125
Y. Hamaya
12. On a Cauchy-Singular Boundary Integral Equation of the First Kind 141
R. Laube
13. Revisiting CSIE in L2: Condition Numbers and Inverse Theorems 159
C. Laurita, G. Mastroianni andM.G. Russo
14. Periodic Boundary Value Problems for First-Order Impulsive
Integro-Differential Equations in Abstract Spaces 185
X. Liu
15. Convergence of Product Integration Rules for Weights on the
Whole Real Line II 201
D. S. Lubinsky
16. Existence Theory for Nonresonant Nonlinear Fredholm Integral Equations
and Nonresonant Operator Equations 217
M. Meehan and D. O’Regan
17. Periodic Boundary Value Problem for Nonlinear First Order
Integro-Ordinary Differential Equations 237
J.J. Nieto, E. Liz and D. Franco
18. Interpolator Quadrature Formulae with Bemstein-Szego Abscissae 247
S. E. Notaris
19. Uniqueness Problems for Some Classes of Nonlinear Volterra Equations 259
W. Okrasiriski
20. Dynamics of a Volterra—Lotka Competition Model with Diffusion
and Time Delays 269
C.V.Pao
21. Hammerstein Integral Inclusions in Banach Spaces 279
N. S. Papageorgiou andN. Yannakakis
CONTENTS ix
22. A Note on Polynomial Interpolation on Holder Spaces 295
U. Schmid
23. Integro-differential Equations and Variational Lyapunov Method 299
S.A.F. Stephens and V. Lakshmikantham
24. A Second Kind Fredholm Integral Equation Arising in Radiative Heat
Exchange 307
D.J. Worth, A. Spence and S.T. Kolaczkowski