Existence Theory For Nonlinear Integral And Integrodifferential Equations PDF Download
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| Author | : Donal O'Regan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 230 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401149925 |
Download Existence Theory for Nonlinear Integral and Integrodifferential Equations Book in PDF, ePub and Kindle
The theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in tegral inclusions, stochastic equations and periodic problems. We note that the selected topics reflect the particular interests of the authors. Donal 0 'Regan Maria Meehan CHAPTER 1 INTRODUCTION AND PRELIMINARIES 1.1. Introduction The aim of this book is firstly to provide a comprehensive existence the ory for integral and integrodifferential equations, and secondly to present some specialised topics in integral equations which we hope will inspire fur ther research in the area. To this end, the first part of the book deals with existence principles and results for nonlinear, Fredholm and Volterra inte gral and integrodifferential equations on compact and half-open intervals, while selected topics (which reflect the particular interests of the authors) such as nonresonance and resonance problems, equations in Banach spaces, inclusions, and stochastic equations are presented in the latter part.
| Author | : Donal O'Regan |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 207 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401715173 |
Download Existence Theory for Nonlinear Ordinary Differential Equations Book in PDF, ePub and Kindle
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
| Author | : R Precup |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 221 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401599866 |
Download Methods in Nonlinear Integral Equations Book in PDF, ePub and Kindle
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 | : Ravi P. Agarwal |
| Publisher | : CRC Press |
| Total Pages | : 344 |
| Release | : 2000-03-09 |
| Genre | : Mathematics |
| ISBN | : 9789056992217 |
Download Integral and Integrodifferential Equations Book in PDF, ePub and Kindle
This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.
| Author | : V. Lakshmikantham |
| Publisher | : CRC Press |
| Total Pages | : 376 |
| Release | : 1995-03-15 |
| Genre | : Mathematics |
| ISBN | : 9782884490009 |
Download Theory of Integro-Differential Equations Book in PDF, ePub and Kindle
This unique monograph investigates the theory and applications of Volterra integro-differential equations. Whilst covering the basic theory behind these equations it also studies their qualitative properties and discusses a large number of applications. This comprehensive work presents a unified framework to investigate the fundamental existence of theory, treats stability theory in terms of Lyapunov functions and functionals, develops the theory of integro-differential equations with impulse effects, and deals with linear evolution equations in abstract spaces. Various applications of integro-differential equations, such as population dynamics, nuclear reactors, viscoelasticity, wave propagation and engineering systems, are discussed, making this book indispensable for mathematicians and engineers alike.
| Author | : Harendra Singh |
| Publisher | : Springer Nature |
| Total Pages | : 255 |
| Release | : 2021-04-16 |
| Genre | : Technology & Engineering |
| ISBN | : 3030655091 |
Download Topics in Integral and Integro-Differential Equations Book in PDF, ePub and Kindle
This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations
| Author | : Feliz Manuel Minhós |
| Publisher | : MDPI |
| Total Pages | : 158 |
| Release | : 2021-04-15 |
| Genre | : Mathematics |
| ISBN | : 3036507108 |
Download Nonlinear Differential Equations and Dynamical Systems Book in PDF, ePub and Kindle
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
| Author | : Jurgen Appell |
| Publisher | : CRC Press |
| Total Pages | : 582 |
| Release | : 2000-02-29 |
| Genre | : Mathematics |
| ISBN | : 9780824703967 |
Download Partial Integral Operators and Integro-Differential Equations Book in PDF, ePub and Kindle
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 | : Abdul-Majid Wazwaz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 639 |
| Release | : 2011-11-24 |
| Genre | : Mathematics |
| ISBN | : 3642214495 |
Download Linear and Nonlinear Integral Equations Book in PDF, ePub and Kindle
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 | : Harold Thayer Davis |
| Publisher | : |
| Total Pages | : 590 |
| Release | : 1960 |
| Genre | : Calculus |
| ISBN | : |
Download Introduction to Nonlinear Differential and Integral Equations Book in PDF, ePub and Kindle
