Multiplicative Differential Equations Volume II

Multiplicative Differential Equations: Volume II is the second 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 is devoted to the theory of multiplicative differential systems. The asymptotic behavior of the solutions of such systems is studied. Stability theory for multiplicative linear and nonlinear systems is introduced and boundary value problems for second-order multiplicative linear and nonlinear equations are explored. The authors also present first-order multiplicative partial differential equations. Each chapter ends with a section of practical problems. The text is accessible to graduate students and researchers in mathematics, physics, engineering and biology.

Preface 1Systems Multiplicative Differential Equations1.1Systems of Multiplicative Linear Differential Equations 1.2nth Order MDE 1.3Multiplicative Homogeneous Systems1.4Multiplicative Fundamental Matrix Solutions1.5Multiplicative Adjoint Systems1.6The Method of Variation of Constants1.7Systems with Multiplicative Constant Coefficients1.8Advanced Practical Exercises2 Qualitative Analysis of Multiplicative Differential Systems2.1Periodic Multiplicative Linear Systems2.2Asymptotic Behaviour of Solutions I 2.3Asymptotic Behaviour of Solutions II2.4Asymptotic Behaviour of Solutions III 2.5Asymptotic Behaviour of Solutions IV 2.6Asymptotic Behaviour of Solutions V2.7Asymptotic Behaviour of Solutions VI 2.8Advanced Practical Problems3 Stability Theory3.1Definition. Examples3.2Criteria for Stability3.3Uniform Stability3.4Stability of Quasi-Multiplicative Linear Systems3.5Two-Dimensional Autonomous Systems3.6Advanced Practical Problems 4Multiplicative Linear Boundary Value Problems4.1Introduction4.2Existence of Solution4.3Multiplicative Green Functions4.4Advanced Practical Problems 5Multiplicative Nonlinear MDEs5.1Multiplicative Lyapunov Direct Method I5.2Multiplicative Lyapunov Direct Method II5.3Multiplicative Nonlinear BVPs5.4Advanced Practical Problems 6First Order MPDE6.1Classification6.2Solvability6.3The Cauchy Problem6.4The Multiplicative Pfaff Equation6.5Some Special Systems6.6Advanced Practical Problems BibliographyIndex

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.