Differential Equations with Maxima - Couverture rigide

Bainov, Drumi D.; Hristova, Snezhana G.

Couverture rigide

ISBN 10 : 1439867577 ISBN 13 : 9781439867570

Editeur : Chapman and Hall/CRC, 2019

Synopsis

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 additiv

A propos du livre

À propos de l?auteur

Drumi D. Bainov, Medical University of Sofia, Bulgaria

Snezhana G. Hristova, Plovdiv University, Bulgaria

Détails de l'édition

• Éditeur: Chapman and Hall/CRC
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 1439867577
• ISBN 13: 9781439867570
• Reliure: Relié
• Nombre de pages: 302
• Coordonnées du fabricant: CRC Press; https://www.routledge-ny.com; ; 6000 BROKEN SOUND PARKWAY, NW SUITE 300; BOCA RATON; FL; 33487; Etats-Unis
• Personne responsable: non disponible