Multiplicative Differential Equations Volume I

Multiplicative Differential Equations: Volume I is the first part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume begins with a basic introduction to multiplicative differential equations and then moves on to first- and second-order equations, as well as the question of existence and uniqueness of solutions. Each chapter ends with a section of practical problems. The book is accessible to graduate students and researchers in mathematics, physics, engineering and biology.

Preface Introduction Definition of MDE Order of MDE Solution of MDE Classification of MDE Basic Problems for MDE Advanced Practical Problems Elementary First Order MDEs Separable First Order MDEs Multiplicative Homogeneous Functions Multiplicative Homogeneous MDE Exact Multiplicative Differential Equations Multiplicative Integrating Factor Advanced Practical Problems First Order Multiplicative Linear Differential Equations Definition. General Solutions The Multiplicative Bernoulli Equation The Multiplicative Riccati Equation Applications Multiplicative Initial Value Problems Some Multiplicative Nonlinear Differential Equations Advanced Practical Problems 4. Second Order Linear MDEs General Properties Multiplicative Linear Dependence The Multiplicative Abel Theorem A Particular Case The Multiplicative Constant Case The Method of Variation of Parameters The Multiplicative Cauchy-Euler Equation Advanced Practical Problems 5. Existence and Uniqueness of Solutions Introduction The Multiplicative Gronwall Type Integral Inequalities Picard’s Method of Successive Approximations and Existence Theorems Uniqueness Continuous Dependence on Initial Data Advanced Practical Problems Bibliography Index

Svetlin G. Georgiev (born 05 April 1974, Rouse, Bulgaria) is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations and dynamic calculus on time scales. Khaled Zennir was born in Skikda, Algeria, in 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbès University, Algeria (Assist. Professor). He obtained his highest diploma in Algeria (Habilitation, Mathematics) from Constantine University, Algeria, in May 2015 (Assoc. Professor). He is now Associate Professor at Qassim University, KSA. His research interests lie in nonlinear hyperbolic partial differential equations: global existence, blow-up and long time behavior.