Nonlinear Integral Operators And Applications
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Author |
: Carlo Bardaro |
Publisher |
: Walter de Gruyter |
Total Pages |
: 214 |
Release |
: 2008-08-22 |
ISBN-10 |
: 9783110199277 |
ISBN-13 |
: 3110199270 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Nonlinear Integral Operators and Applications by : Carlo Bardaro
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 |
: R Precup |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 221 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9789401599863 |
ISBN-13 |
: 9401599866 |
Rating |
: 4/5 (63 Downloads) |
Synopsis Methods in Nonlinear Integral Equations by : R Precup
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 |
: Jurgen Appell |
Publisher |
: CRC Press |
Total Pages |
: 582 |
Release |
: 2000-02-29 |
ISBN-10 |
: 0824703960 |
ISBN-13 |
: 9780824703967 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Partial Integral Operators and Integro-Differential Equations by : Jurgen Appell
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 |
: |
Total Pages |
: 400 |
Release |
: 1964 |
ISBN-10 |
: STANFORD:36105031265056 |
ISBN-13 |
: |
Rating |
: 4/5 (56 Downloads) |
Synopsis Nonlinear Integral Equations by : Philip M. Anselone
Author |
: E.G. Ladopoulos |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 569 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9783662042915 |
ISBN-13 |
: 3662042916 |
Rating |
: 4/5 (15 Downloads) |
Synopsis Singular Integral Equations by : E.G. Ladopoulos
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 |
: Hemen Dutta |
Publisher |
: Springer Nature |
Total Pages |
: 912 |
Release |
: 2019-08-23 |
ISBN-10 |
: 9783030152420 |
ISBN-13 |
: 3030152421 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Current Trends in Mathematical Analysis and Its Interdisciplinary Applications by : Hemen Dutta
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 |
: Israel C. Gohberg |
Publisher |
: Birkhäuser |
Total Pages |
: 333 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034887892 |
ISBN-13 |
: 3034887892 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Differential and Integral Operators by : Israel C. Gohberg
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 |
: Abdul-Majid Wazwaz |
Publisher |
: Springer |
Total Pages |
: 639 |
Release |
: 2011-09-06 |
ISBN-10 |
: 3642214487 |
ISBN-13 |
: 9783642214486 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Linear and Nonlinear Integral Equations by : Abdul-Majid Wazwaz
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 |
: Indur B. Mandhyan |
Publisher |
: |
Total Pages |
: 208 |
Release |
: 1987 |
ISBN-10 |
: OCLC:18264498 |
ISBN-13 |
: |
Rating |
: 4/5 (98 Downloads) |
Synopsis The Diagonalization of Some Nonlinear Integral Operators and Their Computation by : Indur B. Mandhyan
Author |
: Henryk Hudzik |
Publisher |
: CRC Press |
Total Pages |
: 532 |
Release |
: 2000-07-18 |
ISBN-10 |
: 9781482270501 |
ISBN-13 |
: 1482270501 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Function Spaces by : Henryk Hudzik
This volume compiles research results from the fifth Function Spaces International Conference, held in Poznan, Poland. It presents key advances, modern applications and analyses of function spaces and contains two special sections recognizing the contributions and influence of Wladyslaw Orlicz and Genadil Lozanowskii.