# Generalized Ordinary Differential Equations

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### Generalized Ordinary Differential Equations

Author | : ?tefan Schwabik |

Publsiher | : World Scientific |

Total Pages | : 400 |

Release | : 1992 |

Genre | : Mathematics |

ISBN | : 9810212259 |

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The contemporary approach of J Kurzweil and R Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous dependence on parameters for ordinary differential equations. For this purpose, a generalized form of the integral based on integral sums is defined. The theory of generalized differential equations based on this integral is then used, for example, to cover differential equations with impulses or measure differential equations. Solutions of generalized differential equations are found to be functions of bounded variations.The book may be used for a special undergraduate course in mathematics or as a postgraduate text. As there are currently no other special research monographs or textbooks on this topic in English, this book is an invaluable reference text for those interested in this field.

### Generalized Ordinary Differential Equations in Abstract Spaces and Applications

Author | : Everaldo M. Bonotto,Márcia Federson,Jaqueline G. Mesquita |

Publsiher | : John Wiley & Sons |

Total Pages | : 514 |

Release | : 2021-09-15 |

Genre | : Mathematics |

ISBN | : 9781119654933 |

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GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.

### Generalized Ordinary Differential Equations

Author | : Jaroslav Kurzweil |

Publsiher | : World Scientific |

Total Pages | : 208 |

Release | : 2012 |

Genre | : Mathematics |

ISBN | : 9789814324021 |

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This book provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations. It contains many new concepts and results in the framework of a unifying theory. In particular, this new approach is suitable in situations where fast oscillations occur.

### Volterra Stieltjes Integral Equations and Generalized Ordinary Differential Expressions

Author | : A.B. Mingarelli |

Publsiher | : Springer |

Total Pages | : 320 |

Release | : 2006-11-15 |

Genre | : Mathematics |

ISBN | : 9783540398653 |

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### Volterra Stieltjes Integral Equations and Generalized Ordinary Differential Expressions

Author | : A. B. Mingarelli |

Publsiher | : Unknown |

Total Pages | : 336 |

Release | : 2014-01-15 |

Genre | : Electronic Book |

ISBN | : 3662186810 |

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### Generalized Linear Differential Systems

Author | : William T. Reid |

Publsiher | : Unknown |

Total Pages | : 32 |

Release | : 1958 |

Genre | : Fredholm equations |

ISBN | : UOM:39015095253962 |

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### Differential Equations with Discontinuous Righthand Sides

Author | : A.F. Filippov |

Publsiher | : Springer Science & Business Media |

Total Pages | : 322 |

Release | : 1988-09-30 |

Genre | : Mathematics |

ISBN | : 902772699X |

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

### Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations

Author | : R P Agarwal,V Lakshmikantham |

Publsiher | : World Scientific Publishing Company |

Total Pages | : 324 |

Release | : 1993-03-31 |

Genre | : Science |

ISBN | : 9789813104617 |

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This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions. Contents:First Order Differential EquationsFirst Order Differential SystemsHigher Order Differential EquationsDifferential Equations in Abstract SpacesComplex Differential EquationsFunctional Differential EquationsImpulsive Differential EquationsDifferential Equations with HysteresisGeneralized Differential Equations Readership: Applied mathematicians, mathematicians and mathematical physicists.