Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.
Author(s): Pachpatte B.G.
Series: Atlantis studies in mathematics for engineering and science, volume 9
Edition: 1
Publisher: Atlantis Press
Year: 2011
Language: English
Pages: 256
Tags: Математика;Интегральные уравнения;
Cover......Page 1
Atlantis Studies in Mathematics for Engineering and Science 9......Page 2
Multidimensional Integral
Equations and Inequalities......Page 4
Print: 9789491216169......Page 5
Preface......Page 8
Contents......Page 10
Introduction......Page 12
1.2 Basic integral inequalities......Page 20
1.3 Volterra-type integral equation......Page 24
1.4 Volterra-Fredholm-type integral equation......Page 32
1.5 Integrodifferential equations of hyperbolic-type......Page 38
1.6 Fredholm-type integrodifferential equation......Page 48
1.7 Miscellanea......Page 57
1.8 Notes......Page 68
2.2 Integral inequalities in two variables......Page 70
2.3 Integral inequalities in three variables......Page 76
2.4 Integral equation in two variables......Page 84
2.5 Integral equation in three variables......Page 89
2.6 Hyperbolic-type Fredholm integrodifferential equation......Page 94
2.7 Miscellanea......Page 100
2.8 Notes......Page 106
3.2 Volterra-Fredholm-type integral inequalities I......Page 108
3.3 Volterra-Fredholm-type integral inequalities II......Page 119
3.4 Integral equation of Volterra-Fredholm-type......Page 127
3.5 Volterra-Fredholm-type integral equations......Page 133
3.6 General Volterra-Fredholm-type integral equations......Page 139
3.7 Miscellanea......Page 146
3.8 Notes......Page 152
4.2 Basic integral inequalities......Page 154
4.3 Integrodifferential equation of Barbashin-type......Page 158
4.4 General integral equation of Barbashin-type......Page 166
4.5 Integrodifferential equation of the type arising in reactor dynamics......Page 172
4.6 Initial-boundary value problem for integrodifferential equations......Page 180
4.7 Miscellanea......Page 190
4.8 Notes......Page 200
5.2 Sum-difference inequalities in two variables......Page 202
5.3 Sum-difference inequalities in three variables......Page 209
5.4 Multivariable sum-difference inequalities......Page 215
5.5 Sum-difference equations in two variables......Page 222
5.6 Volterra-Fredholm-type sum-difference equations......Page 233
5.7 Miscellanea......Page 239
5.8 Notes......Page 246
Bibliography......Page 248
Subject Index......Page 254
