Existence Theory for Nonlinear Integral and Integrodifferential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Existence Theory for Nonlinear Integral and Integrodifferential Equations write by Donal O'Regan. This book was released on 2012-12-06. Existence Theory for Nonlinear Integral and Integrodifferential Equations available 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.
Existence Theory for Nonlinear Ordinary Differential Equations
Existence Theory for Nonlinear Ordinary Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Existence Theory for Nonlinear Ordinary Differential Equations write by Donal O'Regan. This book was released on 2013-04-17. Existence Theory for Nonlinear Ordinary Differential Equations available 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.
Integral and Integrodifferential Equations
Integral and Integrodifferential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integral and Integrodifferential Equations write by Ravi P. Agarwal. This book was released on 2000-03-09. Integral and Integrodifferential Equations available 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.
Methods in Nonlinear Integral Equations
Methods in Nonlinear Integral Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Methods in Nonlinear Integral Equations write by R Precup. This book was released on 2013-03-09. Methods in Nonlinear Integral Equations available 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.
Nonlinear Differential Equations and Dynamical Systems
Nonlinear Differential Equations and Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Differential Equations and Dynamical Systems write by Feliz Manuel Minhós. This book was released on 2021-04-15. Nonlinear Differential Equations and Dynamical Systems available 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.
