Differential Equations with Maxima

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Opis: Differential Equations with Maxima - Drumi D. Bainov, Snezhana G. Hristova, Drumi Bainov

Differential equations with "maxima"-differential equations that contain the maximum of the unknown function over a previous interval-adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various technical systems on which our ever-advancing, high-tech world depends. Understanding and manipulating the theoretical results and investigations of differential equations with maxima opens the door to enormous possibilities for applications to real-world processes and phenomena. Presenting the qualitative theory and approximate methods, Differential Equations with Maxima begins with an introduction to the mathematical apparatus of integral inequalities involving maxima of unknown functions. The authors solve various types of linear and nonlinear integral inequalities, study both cases of single and double integral inequalities, and illustrate several direct applications of solved inequalities. They also present general properties of solutions as well as existence results for initial value and boundary value problems. Later chapters offer stability results with definitions of different types of stability with sufficient conditions and include investigations based on appropriate modifications of the Razumikhin technique by applying Lyapunov functions. The text covers the main concepts of oscillation theory and methods applied to initial and boundary value problems, combining the method of lower and upper solutions with appropriate monotone methods and introducing algorithms for constructing sequences of successive approximations. The book concludes with a systematic development of the averaging method for differential equations with maxima as applied to first-order and neutral equations. It also explores different schemes for averaging, partial averaging, partially additive averaging, and partially multiplicative averaging. A solid overview of the field, this book guides theoretical and applied researchers in mathematics toward further investigations and applications of these equations for a more accurate study of real-world problems.Introduction Integral Inequalities with Maxima Linear Integral Inequalities with Maxima for Scalar Functions of One Variable Nonlinear Integral Inequalities with Maxima for Scalar Functions of One Variable Integral Inequalities with Maxima for Scalar Functions of Two Variables Applications of the Integral Inequalities with Maxima General Theory Existence Theory for Initial Value Problems Existence Theory for Boundary Value Problems Differential Equations with "Maxima" via Weakly Picard Operator Theory Stability Theory and Lyapunov Functions Stability and Uniform Stability Integral Stability in Terms of Two Measures Stability and Cone Valued Lyapunov Functions Practical Stability on a Cone Oscillation Theory Differential Equations with "Maxima" versus Differential Equations with Delay Oscillations of Delay Differential Equations with "Maxima" Oscillations of Forced n-th Order Differential Equations with "Maxima" Oscillations and Almost Oscillations of n-th Order Differential Equations with "Maxima" Oscillations of Differential Inequalities with "Maxima" Asymptotic Methods Monotone-Iterative Technique for Initial Value Problems Monotone-Iterative Technique for a Periodic Boundary Value Problem Monotone-Iterative Technique for Second Order Differential Equations with "Maxima" Method of Quasilinearization for an Initial Value Problem Method of Quasilinearization for a Periodic Boundary Value Problem Averaging Method Averaging Method for an Initial Value Problem Averaging Method for Multipoint Boundary Value Problem Partial Averaging Method Partially Additive and Partially Multiplicative Averaging Method Notes and Comments Bibliography


Szczegóły: Differential Equations with Maxima - Drumi D. Bainov, Snezhana G. Hristova, Drumi Bainov

Tytuł: Differential Equations with Maxima
Autor: Drumi D. Bainov, Snezhana G. Hristova, Drumi Bainov
Producent: CRC Press Inc.
ISBN: 9781439867570
Rok produkcji: 2011
Ilość stron: 312
Oprawa: Twarda
Waga: 0.56 kg


Recenzje: Differential Equations with Maxima - Drumi D. Bainov, Snezhana G. Hristova, Drumi Bainov

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Differential Equations with Maxima

, ,

Differential equations with "maxima"-differential equations that contain the maximum of the unknown function over a previous interval-adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various technical systems on which our ever-advancing, high-tech world depends. Understanding and manipulating the theoretical results and investigations of differential equations with maxima opens the door to enormous possibilities for applications to real-world processes and phenomena. Presenting the qualitative theory and approximate methods, Differential Equations with Maxima begins with an introduction to the mathematical apparatus of integral inequalities involving maxima of unknown functions. The authors solve various types of linear and nonlinear integral inequalities, study both cases of single and double integral inequalities, and illustrate several direct applications of solved inequalities. They also present general properties of solutions as well as existence results for initial value and boundary value problems. Later chapters offer stability results with definitions of different types of stability with sufficient conditions and include investigations based on appropriate modifications of the Razumikhin technique by applying Lyapunov functions. The text covers the main concepts of oscillation theory and methods applied to initial and boundary value problems, combining the method of lower and upper solutions with appropriate monotone methods and introducing algorithms for constructing sequences of successive approximations. The book concludes with a systematic development of the averaging method for differential equations with maxima as applied to first-order and neutral equations. It also explores different schemes for averaging, partial averaging, partially additive averaging, and partially multiplicative averaging. A solid overview of the field, this book guides theoretical and applied researchers in mathematics toward further investigations and applications of these equations for a more accurate study of real-world problems.Introduction Integral Inequalities with Maxima Linear Integral Inequalities with Maxima for Scalar Functions of One Variable Nonlinear Integral Inequalities with Maxima for Scalar Functions of One Variable Integral Inequalities with Maxima for Scalar Functions of Two Variables Applications of the Integral Inequalities with Maxima General Theory Existence Theory for Initial Value Problems Existence Theory for Boundary Value Problems Differential Equations with "Maxima" via Weakly Picard Operator Theory Stability Theory and Lyapunov Functions Stability and Uniform Stability Integral Stability in Terms of Two Measures Stability and Cone Valued Lyapunov Functions Practical Stability on a Cone Oscillation Theory Differential Equations with "Maxima" versus Differential Equations with Delay Oscillations of Delay Differential Equations with "Maxima" Oscillations of Forced n-th Order Differential Equations with "Maxima" Oscillations and Almost Oscillations of n-th Order Differential Equations with "Maxima" Oscillations of Differential Inequalities with "Maxima" Asymptotic Methods Monotone-Iterative Technique for Initial Value Problems Monotone-Iterative Technique for a Periodic Boundary Value Problem Monotone-Iterative Technique for Second Order Differential Equations with "Maxima" Method of Quasilinearization for an Initial Value Problem Method of Quasilinearization for a Periodic Boundary Value Problem Averaging Method Averaging Method for an Initial Value Problem Averaging Method for Multipoint Boundary Value Problem Partial Averaging Method Partially Additive and Partially Multiplicative Averaging Method Notes and Comments Bibliography

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Cena 368,55 PLN
Nasza cena 344,60 PLN
Oszczędzasz 6%
Wysyłka: Niedostępna
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Szczegóły: Differential Equations with Maxima - Drumi D. Bainov, Snezhana G. Hristova, Drumi Bainov

Tytuł: Differential Equations with Maxima
Autor: Drumi D. Bainov, Snezhana G. Hristova, Drumi Bainov
Producent: CRC Press Inc.
ISBN: 9781439867570
Rok produkcji: 2011
Ilość stron: 312
Oprawa: Twarda
Waga: 0.56 kg


Recenzje: Differential Equations with Maxima - Drumi D. Bainov, Snezhana G. Hristova, Drumi Bainov

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