Nonlinear Higher Order Differential And Integral Coupled Systems Impulsive And Integral Equations On Bounded And Unbounded Domains

Author : Feliz Manuel Minhos,Robert De Sousa
Publisher : World Scientific
Page : 243 pages
File Size : 53,9 Mb
Release : 2022-04-11
Category : Mathematics
ISBN : 9789811225147

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Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains by Feliz Manuel Minhos,Robert De Sousa Pdf

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.

Author : Gangaram S Ladde,Masilamani Sambandham
Publisher : World Scientific
Page : 355 pages
File Size : 47,5 Mb
Release : 2024-04-22
Category : Mathematics
ISBN : 9789811287497

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Stochastic Versus Deterministic Systems Of Iterative Processes by Gangaram S Ladde,Masilamani Sambandham Pdf

Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.

Author : A M Samoilenko,N A Perestyuk
Publisher : World Scientific
Page : 472 pages
File Size : 44,5 Mb
Release : 1995-08-31
Category : Science
ISBN : 9789814499828

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Impulsive Differential Equations by A M Samoilenko,N A Perestyuk Pdf

Contents:General Description of Impulsive Differential SystemsLinear SystemsStability of SolutionsPeriodic and Almost Periodic Impulsive SystemsIntegral Sets of Impulsive SystemsOptimum Control in Impulsive SystemsAsymptotic Study of Oscillations in Impulsive SystemsA Periodic and Almost Periodic Impulsive SystemsBibliographySubject Index Readership: Researchers in nonlinear science. keywords:Differential Equations with Impulses;Linear Systems;Stability;Periodic and Quasi-Periodic Solutions;Integral Sets;Optimal Control “… lucid … the book … will benefit all who are interested in IDE…” Mathematics Abstracts

Author : Anonim
Publisher : Unknown
Page : 1208 pages
File Size : 47,9 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015078588608

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Mathematical Reviews by Anonim Pdf

Author : Dajun Guo,Yeol Je Cho,Jiang Zhu
Publisher : Nova Publishers
Page : 362 pages
File Size : 41,8 Mb
Release : 2004
Category : Mathematics
ISBN : 1594540187

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Partial Ordering Methods in Nonlinear Problems by Dajun Guo,Yeol Je Cho,Jiang Zhu Pdf

Special Interest Categories: Pure and applied mathematics, physics, optimisation and control, mechanics and engineering, nonlinear programming, economics, finance, transportation and elasticity. The usual method used in studying nonlinear problems such as topological method, variational method and others are generally only suited to the nonlinear problems with continuity and compactness. However, a lots of the problems appeared in theory and applications have no continuity and compactness, For example, differential equations and integral equations in infinite dimensional spaces, various equations defined on unbounded region are generally having no compactness. The problems can been divided into three types as follows: (1) Without using compact conditions but only using some inequalities related to some ordering, the existence and uniqueness of the fixed point for increasing operators, decreasing operators and mixed monotone operators, and the convergence of the iterative sequence are obtained. Also, these results have been used to nonlinear integral equations defined on unbounded regions. (2) Without using continuity conditions but only using a very relaxed weakly compact conditions, some new fixed point theorem of increasing operators are obtained. We have applied these results to nonlinear equations with discontinuous terms. (3) They systemly use the partial ordering methods to nonlinear integro-differential equations (include impulsive type) in Banach space.

Author : Dajun Guo,V. Lakshmikantham,Xinzhi Liu
Publisher : Springer
Page : 344 pages
File Size : 43,5 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 146128547X

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Nonlinear Integral Equations in Abstract Spaces by Dajun Guo,V. Lakshmikantham,Xinzhi Liu Pdf

Many problems arising in the physical sciences, engineering, biology and ap plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul sive differential equations in Banach spaces.

Author : Irena Rachůnková,Jan Tomeček
Publisher : Springer
Page : 190 pages
File Size : 48,5 Mb
Release : 2015-09-29
Category : Mathematics
ISBN : 9789462391277

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State-Dependent Impulses by Irena Rachůnková,Jan Tomeček Pdf

This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.

Author : Nikolaĭ Alekseevich Peresti͡uk
Publisher : Walter de Gruyter
Page : 325 pages
File Size : 49,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110218169

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Differential Equations with Impulse Effects by Nikolaĭ Alekseevich Peresti͡uk Pdf

This monograph is an introduction to the theory of ordinary differential equations with jump conditions at discrete moments of time. From the contents: Pulse differential equations and inclusions Linear systems with multivalued trajectories Method of averaging in systems with pulse action Averaging of differential inclusions Differential equa

Author : Efim Natanovich Rozenvasser
Publisher : Unknown
Page : 530 pages
File Size : 53,5 Mb
Release : 1971
Category : Integral equations
ISBN : WISC:89038743134

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Vibrations of Nonlinear Systems by Efim Natanovich Rozenvasser Pdf

Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not related to each other have been developed at the present time. The book deals with a systematic examination of several applied problems in the theory of nonlinear oscillations using the method of integral equations. By this approach it proves possible to establish an intimate relationship between small-parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to give the latter a rigorous foundation. All the results thus obtained are applicable to a broad class of systems described by nonlinear operator equations. The book also considers certain problems of periodic oscillations unrelated to the use of integral equations.

Author : R. Reissig,G. Sansone,R. Conti
Publisher : Springer
Page : 696 pages
File Size : 52,8 Mb
Release : 1974-01-31
Category : Mathematics
ISBN : UCAL:B3990448

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Non-Linear Differential Equations of Higher Order by R. Reissig,G. Sansone,R. Conti Pdf

Author : James A. Yorke
Publisher : Springer
Page : 282 pages
File Size : 47,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540363064

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Seminar on Differential Equations and Dynamical Systems by James A. Yorke Pdf

Author : Kuppalapalle Vajravelu
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 44,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302773

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Differential Equations and Nonlinear Mechanics by Kuppalapalle Vajravelu Pdf

The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Aerospace Engineering, and the Office of International Studies (of the University of Central Florida) for the financial support of the conference. Also, to the Mathematics Department of the University of Central Florida for providing secretarial and administrative assistance. I would like to thank the members of the local organizing committee, Jeanne Blank, Jackie Callahan, John Cannon, Holly Carley, Brad Pyle, Pete Rautenstrauch, and June Wingler for their assistance. Thanks are also due to the conference organizing committee, F. H. Busse, J. R. Cannon, V. Girault, R. H. J. Grimshaw, P. N. Kaloni, V.

Author : Kevin E.M. Church,Xinzhi Liu
Publisher : Springer Nature
Page : 388 pages
File Size : 49,6 Mb
Release : 2021-03-24
Category : Mathematics
ISBN : 9783030645335

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Bifurcation Theory of Impulsive Dynamical Systems by Kevin E.M. Church,Xinzhi Liu Pdf

This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.

Author : D.L. Colton,R.P. Gilbert
Publisher : Springer
Page : 488 pages
File Size : 52,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540373025

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Constructive and Computational Methods for Differential and Integral Equations by D.L. Colton,R.P. Gilbert Pdf

Author : Drumi D Bainov,Valery Covachev
Publisher : World Scientific
Page : 282 pages
File Size : 52,7 Mb
Release : 1994-12-16
Category : Mathematics
ISBN : 9789814504010

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Impulsive Differential Equations With A Small Parameter by Drumi D Bainov,Valery Covachev Pdf

This book is devoted to impulsive differential equations with a small parameter. It consists of three chapters. Chapter One serves as an introduction. In Chapter Two, regularly perturbed impulsive differential equations are considered. Modifications of the method of small parameter, the averaging method, and the method of integral manifolds are proposed. In Chapter Three, singularly perturbed differential equations are considered. A modification of the method of boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated, such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method.The book is written clearly, strictly, and understandably. It is intended for mathematicians, physicists, chemists, biologists and economists, as well as for senior students of these specialities.