Bücher der Reihe Atlantis Studies in Differential Equations

The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics.

In this monograph the author presents explicit conditions for the exponential, absolute and input-to-state stabilities including solution estimates of certain types of functional differential equations.The main methodology used is based on a combination of recent norm estimates for matrix-valued functions, comprising the generalized Bohl-Perron principle, together with its integral version and the positivity of fundamental solutions.A significant part of the book is especially devoted to the solution of the generalized Aizerman problem.

The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level.

The presentation is focused on the issues of existence and uniqueness of solutions in appropriate function spaces and on the study of the specific qualitative properties of solutions, such as localization in space and time, extinction in a finite time and blow-up, or nonexistence of global in time solutions.