Nonlinear Integral Operators And Applications

Author : Carlo Bardaro,Julian Musielak,Gianluca Vinti
Publisher : Walter de Gruyter
Page : 214 pages
File Size : 41,9 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110199277

Get Book

Nonlinear Integral Operators and Applications by Carlo Bardaro,Julian Musielak,Gianluca Vinti Pdf

In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity. This book represents the first attempt at a comprehensive treatment of approximation theory by means of nonlinear integral operators in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed in order to obtain consistent approximation results. Applications to nonlinear summability, nonlinear integral equations and nonlinear sampling theory are given. In particular, the study of nonlinear sampling operators is important since the results permit the reconstruction of several classes of signals. In a wider context, the material of this book represents a starting point for new areas of research in nonlinear analysis. For this reason the text is written in a style accessible not only to researchers but to advanced students as well.

Author : Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko
Publisher : CRC Press
Page : 582 pages
File Size : 43,7 Mb
Release : 2000-02-29
Category : Mathematics
ISBN : 0824703960

Get Book

Partial Integral Operators and Integro-Differential Equations by Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko Pdf

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.

Author : Philip M. Anselone
Publisher : Unknown
Page : 400 pages
File Size : 55,5 Mb
Release : 1964
Category : Mathematics
ISBN : STANFORD:36105031265056

Get Book

Nonlinear Integral Equations by Philip M. Anselone Pdf

Author : Israel C. Gohberg,Reinhard Mennicken,Christiane Tretter
Publisher : Birkhäuser
Page : 333 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887892

Get Book

Differential and Integral Operators by Israel C. Gohberg,Reinhard Mennicken,Christiane Tretter Pdf

This and the next volume of the OT series contain the proceedings of the Work shop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob lems, starting with problems for abstract operators up to spectral theory of ordi nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems.

Author : Hemen Dutta,Ljubiša D. R. Kočinac,Hari M. Srivastava
Publisher : Springer Nature
Page : 912 pages
File Size : 41,8 Mb
Release : 2019-08-23
Category : Mathematics
ISBN : 9783030152420

Get Book

Current Trends in Mathematical Analysis and Its Interdisciplinary Applications by Hemen Dutta,Ljubiša D. R. Kočinac,Hari M. Srivastava Pdf

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 46,9 Mb
Release : 2011-11-24
Category : Mathematics
ISBN : 9783642214493

Get Book

Linear and Nonlinear Integral Equations by Abdul-Majid Wazwaz Pdf

Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.

Author : R Precup
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 53,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401599863

Get Book

Methods in Nonlinear Integral Equations by R Precup Pdf

Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.

Author : Athanass Kartsatos
Publisher : CRC Press
Page : 338 pages
File Size : 48,9 Mb
Release : 1996-03-14
Category : Mathematics
ISBN : 0824797213

Get Book

Theory and Applications of Nonlinear Operators of Accretive and Monotone Type by Athanass Kartsatos Pdf

This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.

Author : Ravi P. Agarwal,Maria Meehan,Donal O'Regan
Publisher : Nova Publishers
Page : 376 pages
File Size : 41,7 Mb
Release : 2001
Category : Mathematics
ISBN : 1590330943

Get Book

Nonlinear Integral Equations and Inclusions by Ravi P. Agarwal,Maria Meehan,Donal O'Regan Pdf

Author : François Trèves,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 45,6 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821814697

Get Book

Pseudodifferential Operators and Applications by François Trèves,American Mathematical Society Pdf

"Proceedings of the Symposium on Pseudodifferential Operators and Fourier Integral Operators with Applications to Partial Differential Equations held at the University of Notre Dame, Notre Dame, Indiana, April 2-5, 1984"--T.p. verso.

Author : Nicolae H. Pavel
Publisher : Springer
Page : 292 pages
File Size : 44,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540471868

Get Book

Nonlinear Evolution Operators and Semigroups by Nicolae H. Pavel Pdf

This research monograph deals with nonlinear evolution operators and semigroups generated by dissipative (accretive), possibly multivalued operators, as well as with the application of this theory to partial differential equations. It shows that a large class of PDE's can be studied via the semigroup approach. This theory is not available otherwise in the self-contained form provided by these Notes and moreover a considerable part of the results, proofs and methods are not to be found in other books. The exponential formula of Crandall and Liggett, some simple estimates due to Kobayashi and others, the characterization of compact semigroups due to Brézis, the proof of a fundamental property due to Ursescu and the author and some applications to PDE are of particular interest. Assuming only basic knowledge of functional analysis, the book will be of interest to researchers and graduate students in nonlinear analysis and PDE, and to mathematical physicists.

Author : David E. Edmunds,V.M Kokilashvili,Alexander Meskhi
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 54,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599221

Get Book

Bounded and Compact Integral Operators by David E. Edmunds,V.M Kokilashvili,Alexander Meskhi Pdf

The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).

Author : Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit
Publisher : Springer Nature
Page : 311 pages
File Size : 46,7 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9789811396083

Get Book

Mathematical Modelling, Applied Analysis and Computation by Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit Pdf

This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.

Author : E.G. Ladopoulos
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 41,9 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9783662042915

Get Book

Singular Integral Equations by E.G. Ladopoulos Pdf

The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Author : Louis B. Rall
Publisher : Elsevier
Page : 595 pages
File Size : 51,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483272443

Get Book

Nonlinear Functional Analysis and Applications by Louis B. Rall Pdf

Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field. Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve. This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.