Second Order Differential Equations In Banach Space

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Second Order Linear Differential Equations In Banach Spaces

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Author : H.O. Fattorini
language : en
Publisher: Elsevier
Release Date : 2011-08-18

Second Order Linear Differential Equations In Banach Spaces written by H.O. Fattorini and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

Second Order Differential Equations In Banach Space

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Author :
language : en
Publisher:
Release Date :

Second Order Differential Equations In Banach Space written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

The theory of second-order differential equations in Banach space is surveyed. An introduction of certain selected aspects of the subject is attempted, rather than a complete discussion. References to various proofs are given, but not the proofs themselves. The bulk of the material concerns linear second-order differential equations, a subject linked intimately with the theory of strongly continuous cosine families of bounded linear operators in Banach space. Results are also presented on nonlinear second-order equations having a special semilinear form. The following topics are included: the basic theory of strongly continuous cosine families in Banach space, and the fundamental generation theorem of Sova--Da Prato--Giusti--Fattorini; the problem of converting an abstract second-order linear differential equation to an abstract first-order differential system; perturbations of the infinitesimal generator of a strongly continuous cosine family, and the approximation theorem of Konishi--Goldstein; the special properties of compactness, uniform continuity, and inhomogeneous equations for strongly continuous cosine families; and abstract semilinear second-order initial-value problems in which the linear term is a cosine family generator. (RWR).

Complete Second Order Linear Differential Equations In Hilbert Spaces

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Author : Alexander Ya. Shklyar
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Complete Second Order Linear Differential Equations In Hilbert Spaces written by Alexander Ya. Shklyar and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood.

Differential Equations And Applications

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Author : Yeol Je Cho
language : en
Publisher: Nova Publishers
Release Date : 2007-07-02

Differential Equations And Applications written by Yeol Je Cho and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-02 with Mathematics categories.

Preface; Existence for set Differential Equations via Multivalued Operator Equations; Nonlocal Cauchy Problem for Abstract Functional Integrodifferential Equations; Existence Results for Discontinuous Functional Evolution Equations in Abstract Spaces; A Generalised Solution of the Black-Scholes Partial Differential Equation; Optimality and Duality for Multiobjective Fractional Programming with Generalised Invexity; Markovian Approach to the Backward Recurrence Time; A Multiplicity Result of Singular Boundary Value Problems for Second Order Impulsive Differential Equations; Extremal Solutions of Initial Value Problem for Non-linear Second Order Impulsive Integro-Differential Equations of Volterra Type in Banach Spaces; Construction of Upper and Lower Solutions for Singular p-Laplacian Equations with Sign Changing Nonlinearities; A Qualitative Hamiltonian Model for Human Motion; ; Newton's Method for Matrix Polynomials; Admissibility and Non-Uniform Dichotomy for Differential Systems; Boundary Value Problems of Fuzzy Differential Equations on an Infinite Interval; An Ultimate Boundedness Result for a Certain System of Fourth Order Non-linear Differential Equations; The Initial Value Problems for the First Order System of Non-linear Impulsive Integro-Differential Equations; Generic Well-Posedness of Nonconvex Optimal Control Problems; Index.

Second Order Partial Differential Equations In Hilbert Spaces

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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2002-07-25

Second Order Partial Differential Equations In Hilbert Spaces written by Giuseppe Da Prato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.

State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.

Differential Equations In Banach Spaces

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Author : Giovanni Dore
language : en
Publisher: CRC Press
Release Date : 2020-10-07

Differential Equations In Banach Spaces written by Giovanni Dore and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.

This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.

Exponentially Convergent Algorithms For Abstract Differential Equations

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Author : Ivan Gavrilyuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-17

Exponentially Convergent Algorithms For Abstract Differential Equations written by Ivan Gavrilyuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-17 with Mathematics categories.

This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.

Linear Differential Equations In Banach Space

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Author : S. G. Kreui
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-07-14

Linear Differential Equations In Banach Space written by S. G. Kreui and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-14 with Mathematics categories.

Topological Methods In Differential Equations And Inclusions

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Author : Andrzej Granas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Topological Methods In Differential Equations And Inclusions written by Andrzej Granas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.

Boundary Value Problems For Second Order Differential Equations In A Banach Space I

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Author : S. G. Krein
language : en
Publisher:
Release Date : 1967

Boundary Value Problems For Second Order Differential Equations In A Banach Space I written by S. G. Krein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.

It is indicated that a series of problems in mathematical physics (theory of wave-guides, hydrodynamics, and others) can be considered as boundary-value problems for the second-order equation the second derivative of u with respect to t = Au-f(t), 0 = or