Download or read book Constant Sign Solutions of Systems of Integral Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-09-21 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a complete and self-contained account of the theory, methods, and applications of constant-sign solutions of integral equations. In particular, the focus is on different systems of Volterra and Fredholm equations. The presentation is systematic and the material is broken down into several concise chapters. An introductory chapter covers the basic preliminaries. Throughout the book many examples are included to illustrate the theory. The book contains a wealth of results that are both deep and interesting. This unique book will be welcomed by mathematicians working on integral equations, spectral theory, and on applications of fixed point theory and boundary value problems.
Download or read book Topological Methods for Differential Equations and Inclusions written by John R. Graef and published by CRC Press. This book was released on 2018-09-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.
Download or read book Nonlinear Higher Order Differential And Integral Coupled Systems Impulsive And Integral Equations On Bounded And Unbounded Domains written by Feliz Manuel Minhos and published by World Scientific. This book was released on 2022-04-11 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.
Download or read book Integral Equations and Their Applications written by Matiur Rahman and published by WIT Press. This book was released on 2007 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.
Download or read book Volterra Integral Equations written by Hermann Brunner and published by Cambridge University Press. This book was released on 2017-01-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.
Download or read book An Introduction to the Study of Integral Equations written by Maxime Bôcher and published by . This book was released on 1909 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Classical Theory of Integral Equations written by Stephen M. Zemyan and published by Springer Science & Business Media. This book was released on 2012-07-10 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter; Thorough discussions of the analytical methods used to solve many types of integral equations; An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations; Over 80 illustrative examples that are explained in meticulous detail; Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts; Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.
Download or read book Recent Developments in Fixed Point Theory written by Mudasir Younis and published by Springer Nature. This book was released on with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Communications in Applied Analysis written by and published by . This book was released on 2008 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Differential Problems with Smooth and Nonsmooth Constraints written by Dumitru Motreanu and published by Academic Press. This book was released on 2018-02-05 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references. Builds from functional analysis and operator theory, to nonlinear elliptic systems and control problems Outlines the evolution of the main ideas of nonlinear analysis and their roots in classical mathematics Presented with numerous end-of-chapter exercises and sophisticated open problems Illustrated with pertinent industrial and engineering numerical examples and applications Accompanied by hundreds of curated references, saving readers hours of research in conducting literature analysis
Download or read book Linear Integral Equations written by William Vernon Lovitt and published by . This book was released on 1924 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Journal of Integral Equations and Applications written by and published by . This book was released on 2012 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on the Theory of Integral Equations written by I. G. Petrovskii and published by Courier Corporation. This book was released on 1996-09-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple, clear exposition of the Fredholm theory for integral equations of the second kind of Fredholm type. A brief treatment of the Volterra equation is also included. An outstanding feature is a table comparing finite dimensional spaces to function spaces. ". . . An excellent presentation."—Am. Math. Monthly. Translated from second revised (1951) Russian edition. Bibliography.
Download or read book Applied Integral Equations written by Ramakanta Meher and published by Sciendo. This book was released on 2021-08-03 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a vital role of differential and integral equations in studying different types of real-world problems to study the behavior of the issues. Thus, it becomes essential to know the various methods of finding solutions of the integral equation in explicit form. For the integral equations whose solutions cannot be found in explicit form, one has to study the properties of solutions of the given differential equation to guess an approximate solution. This textbook entitled "Applied Integral Equations" is intended to study the methods of finding the explicit solutions of integral equations where ever possible and in the absence of finding an exact solution. It is intended to study the properties of solutions of the given integral equations. This book contains 08 chapters. Chapter-1 discusses the introduction to integral equations, classification of integral equations, Relation between linear differential equations and Volterra integral equation, Nonlinear equation and solution of an integral equation. Chapter-2 discusses the existence and uniqueness theorems of Integral equations, Successive approximation, Iterated Functions, Reciprocal functions, Volterra Solution of Fredholm's equation, Discontinuous Solution, Fredholm equations with separable kernels and Resolvent Kernel. Chapter-3 discusses the Fredholm equation as a limit of a finite system of linear equations, Hadamard's Theorem, Fredholm's two fundamental relations, Fredholm's solution of the Integral equation for different, Characteristic numbers and basic functions, the associated Homogenous integral equations, the orthogonality theorem, Kernels of the form, Eigen Values and eigenfunctions, Fredholm integral equation of the second kind, Eigenvalues for non-separable kernels, Volterra Integral Equation, Solution by the Resolvent kernel and Method of successive approximation. Chapter-4 discusses the Applications of Fredholm theory, Free vibration of an elastic string, The differential equation of the problem, Reduction to a dimensional BVP, Solution of the boundary value problem, Construction of Green function, Equivalence between the Boundary value problem and Linear integral equations, Constrained vibrations of an elastic String, Equivalence between boundary value problem and Linear integral equations and Remark on the solution of the BVP. Chapter-5 discusses the Hilbert-Schmidt Theory that includes Iterations of symmetric kernels, Orthogonality theorem, An existence theorem for the nonlinear integral equation of Fredholm type and the equation of Bratu. Chapter-6 discusses the Fredholm alternatives, An example of Picard's method, Powers of an integral operator, Iterated kernels, Neumann series, A remark on the convergence of the iterative method, Differentiation of function under an integral sign, Relation between differential and integral equation, The Fredholm alternatives and the Fredholm alternative theorem. Chapter-7 discusses the method of undetermined coefficients that includes approximation methods of undetermined coefficients, the method of collocation, the method of weighting functions, the method of least squares and approximation of the kernel. This book is based on syllabi of the theory of integral equations prescribed for the undergraduate and postgraduate students of mathematics and PhD students in different institutions and universities of India and abroad. This book will be helpful for the competitive examinations as well.
Download or read book Applied Singular Integral Equations written by B. N. Mandal and published by CRC Press. This book was released on 2016-04-19 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.
Download or read book Integral Equations written by S. G. Mikhlin and published by Elsevier. This book was released on 2014-07-22 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.
