Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.  To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditionsDiscusses second order difference equations with multi-point boundary conditionsIntroduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions

Science & Math

Luca, Rodica

Henderson, Johnny

Mathematics

Elsevier

Watching Monty

Johnny Henderson spent four years during the Second World War as aide de camp to one of Britain's most famous soldiers of the twentieth century, General Bernard Montgomery - or 'Monty' as he was popularly known. Shortly before he died in 2003, Henderson wrote about his time with Monty at Tac HQ. His account takes the form of a series of insightful anecdotes and brief pen sketches that give a fascinating and often humorous window on life with Monty and those with whom he worked, or came into contact with, during the war years. These people range from King George VI, Winston Churchill and Sir Alan Brooke, to Eisenhower and the German surrender delegation on Luneberg Heath. Drawing on his own unpublished private photograph albums and the photographic collections of the Imperial War Museum, Johnny Henderson relates his time as Monty's ADC, from the Western Desert to Berlin, in the form of a photographic anecdotal scrap book. His pithy observations of life at Tac HQ make a unique contribution to our understanding of what made Monty 'tick', and shows us a less well-known but lighter side of the great man.

Biographies & Memoirs

Douglas-Home, Jamie

Leaders & Notable People

Sutton Pub Ltd

Johnny Henderson spent four years during the Second World War as aide de camp to one of BritainÆs most famous soldiers of the twentieth century, General Bernard Montgomery û or æMontyÆ as he was popularly known. Shortly before he died in 2003, Henderson wrote about his time with Monty at Tac HQ. His account takes the form of a series of insightful anecdotes and brief pen sketches that give a fascinating and often humorous window on life with Monty and those with whom he worked, or came into contact with, during the war years. These people range from King George VI, Winston Churchill and Sir Alan Brooke, to Eisenhower and the German surrender delegation on Luneberg Heath. Drawing on his own unpublished private photograph albums and the photographic collections of the Imperial War Museum, Johnny Henderson relates his time as MontyÆs ADC, from the Western Desert to Berlin, in the form of a photographic anecdotal scrap book. His pithy observations of life at Tac HQ make a unique contribution to our understanding of what made Monty ætickÆ, and shows us a less well-known but lighter side of the great man.

History

Military

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

Topological Methods for Differential Equations and Inclusions (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Graef, John R.

Ouahab, Abdelghani

CRC-Press

Johnny Henderson spent four years during the Second World War as aide-de-camp to one of Britain's most famous soldiers of the twentieth century, General Bernard Montgomery - or 'Monty' as he was popularly known. Shortly before he died in 2003, Henderson wrote about his time with Monty at Tac HQ. His account takes the form of a series of insightful anecdotes and brief pen sketches that give a fascinating and often humorous window on life with Monty and those with whom he worked, or came into contact with, during the war years. These people range from King George VI, Winston Churchill and Sir Alan Brooke, to Eisenhower and the German surrender delegation on Luneberg Heath. Drawing on his own unpublished private photograph albums and the photographic collections of the Imperial War Museum, Johnny Henderson relates his time as Monty's ADC, from the Western Desert to Berlin, in the form of a photographic anecdotal scrap book. His pithy observations of life at Tac HQ make a unique contribution to our understanding of what made Monty 'tick', and shows us a less well-known but lighter side of the great man.

Watching Monty: The Everyday Life of General Bernard Montgomery

Historical

The History Press

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models.  During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Impulsive Differential Inclusions: A Fixed Point Approach (De Gruyter Series in Nonlinear Analysis and Applications, 20)

Walter de Gruyter

This book deals with existence and stability issues for solutions to initial and boundary value problems for functional differential and integral equations and inclusions with Caputo's fractional derivative and Hadamard's fractional integral. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus.

Implicit Fractional Differential and Integral Equations: Existence and Stability (De Gruyter Series in Nonlinear Analysis and Applications, 26)

Abbas, Saïd

Benchohra, Mouffak

de Gruyter

This is an indispensable reference for those mathematicians that conduct research activity in applications of fixed-point theory to boundary value problems for nonlinear difference equations. Coverage includes second-order finite difference equations and systems of second-order finite difference equations subject to diverse multi-point boundary conditions, and various methods to study the existence of positive solutions for these problems.

Boundary Value Problems for Second-Order Finite Difference Equations and Systems (De Gruyter Studies in Mathematics, 91)

ORDINARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS - VOLUME II: BOUNDARY VALUE PROBLEMS (Trends in Abstract and Applied Analysis)

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems (Trends in Abstract and Applied Analysis)

Kong, Lingju

Liu, Xueyan Sherry

WSPC

ORDINARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS - VOLUME I: ADVANCED ORDINARY DIFFERENTIAL EQUATIONS (Trends in Abstract and Applied Analysis)

The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book. The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well. Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems. Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs.

Ordinary Differential Equations And Boundary Value Problems - Volume I: Advanced Ordinary Differential Equations (Trends in Abstract and Applied Analysis)

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