Second Order Linear Differential Equations In Banach Spaces

Author : H.O. Fattorini
Publisher : Elsevier
Page : 313 pages
File Size : 40,6 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080872190

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Second Order Linear Differential Equations in Banach Spaces by H.O. Fattorini Pdf

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.

Author : Alexander Ya. Shklyar
Publisher : Birkhäuser
Page : 225 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034891875

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Complete Second Order Linear Differential Equations in Hilbert Spaces by Alexander Ya. Shklyar Pdf

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.

Author : S. G. Kreui
Publisher : American Mathematical Soc.
Page : 398 pages
File Size : 55,8 Mb
Release : 2011-07-14
Category : Mathematics
ISBN : 9780821869031

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Linear Differential Equations in Banach Space by S. G. Kreui Pdf

Author : Giovanni Dore
Publisher : CRC Press
Page : 289 pages
File Size : 46,6 Mb
Release : 2020-10-07
Category : Mathematics
ISBN : 9781000117103

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Differential Equations in Banach Spaces by Giovanni Dore Pdf

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.

Author : Angelo Favini,Atsushi Yagi
Publisher : CRC Press
Page : 336 pages
File Size : 53,6 Mb
Release : 1998-09-10
Category : Mathematics
ISBN : 9781482276022

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Degenerate Differential Equations in Banach Spaces by Angelo Favini,Atsushi Yagi Pdf

This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the an

Author : Giuseppe Da Prato,Jerzy Zabczyk
Publisher : Cambridge University Press
Page : 397 pages
File Size : 53,9 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 9781139433433

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Second Order Partial Differential Equations in Hilbert Spaces by Giuseppe Da Prato,Jerzy Zabczyk Pdf

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.

Author : Yeol Je Cho
Publisher : Nova Publishers
Page : 182 pages
File Size : 53,9 Mb
Release : 2007-07-02
Category : Mathematics
ISBN : 1594548781

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Differential Equations and Applications by Yeol Je Cho Pdf

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.

Author : KREIN
Publisher : Springer Science & Business Media
Page : 112 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468480689

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Linear Equations in Banach Spaces by KREIN Pdf

INTRODUCTION . . . . . . xiii § 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 § 2. EQUATIONS WITH A CLOSED OPERATOR 6 § 3. THE ADJOINT EQUATION . . . . . . 10 § 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 § 5. AN EQUATION WITH A CLOSED OPERATOR WHICH HAS A DENSE DOMAIN 18 NORMALLY SOLVABLE EQUATIONS WITH FINITE DIMENSIONAL KERNEL. 22 § 6. A PRIORI ESTIMATES .. . . . . . 24 § 7. EQUATIONS WITH FINITE DEFECT . . . 27 § 8. § 9. SOME DIFFERENT ADJOINT EQUATIONS . 30 § 10. LINEAR TRANSFORMATIONS OF EQUATIONS 33 TRANSFORMATIONS OF d-NORMAL EQUATIONS . 38 § 11. § 12. NOETHERIAN EQUATIONS. INDEX. . . . . . 42 § 13. EQUATIONS WITH OPERATORS WHICH ACT IN A SINGLE SPACE 44 § 14. FREDHOLM EQUATIONS. REGULARIZATION OF EQUATIONS 46 § 15. LINEAR CHANGES OF VARIABLE . . . . . . . . 50 § 16. STABILITY OF THE PROPERTIES OF AN EQUATION 53 OVERDETERMINED EQUATIONS 59 § 17. § 18. UNDETERMINED EQUATIONS 62 § 19. INTEGRAL EQUATIONS . . . 65 DIFFERENTIAL EQUATIONS . 80 § 20. APPENDIX. BASIC RESULTS FROM FUNCTIONAL ANALYSIS USED IN THE TEXT 95 LITERATURE CITED . . . . . . . . . . . . . . . . . . .. . . . 99 . . PRE F ACE The basic material appearing in this book represents the substance v of a special series of lectures given by the author at Voronez University in 1968/69, and, in part, at Dagestan University in 1970.

Author : K. Deimling
Publisher : Unknown
Page : 148 pages
File Size : 54,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662162202

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Ordinary Differential Equations in Banach Spaces by K. Deimling Pdf

Author : Angelo Favini,Enrico Obrecht
Publisher : Springer
Page : 309 pages
File Size : 55,7 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540473503

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Differential Equations in Banach Spaces by Angelo Favini,Enrico Obrecht Pdf

Author : Andrzej Granas,Marlène Frigon
Publisher : Springer Science & Business Media
Page : 531 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401103398

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Topological Methods in Differential Equations and Inclusions by Andrzej Granas,Marlène Frigon Pdf

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.

Author : Ju. L. Daleckii,Mark Grigor_evich Kre_n
Publisher : American Mathematical Soc.
Page : 396 pages
File Size : 50,8 Mb
Release : 2002-03-15
Category : Mathematics
ISBN : 9780821832387

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Stability of Solutions of Differential Equations in Banach Space by Ju. L. Daleckii,Mark Grigor_evich Kre_n Pdf

Author : Selim Grigorʹevich Kreĭn
Publisher : Unknown
Page : 398 pages
File Size : 47,8 Mb
Release : 1971
Category : Banach spaces
ISBN : 147041628X

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Linear Differential Equations in Banach Space by Selim Grigorʹevich Kreĭn Pdf

Author : Ti-Jun Xiao,Jin Liang
Publisher : Springer
Page : 314 pages
File Size : 42,6 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783540494799

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The Cauchy Problem for Higher Order Abstract Differential Equations by Ti-Jun Xiao,Jin Liang Pdf

The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.

Author : Robert H. Martin
Publisher : Unknown
Page : 464 pages
File Size : 43,9 Mb
Release : 1987
Category : Banach Spaces
ISBN : UCR:31210007032897

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Nonlinear Operators and Differential Equations in Banach Spaces by Robert H. Martin Pdf