Method of guiding functions in problems of nonlinear analysis
The monograph under review concerns the method of guiding functions (MGF) for solving problems of periodic oscillations in nonlinear systems. The principal subject consists in a comprehensive treatment of the branches of the applications of the MGF in problems of contemporary nonlinear analysis. The main body of the book is divided into five chapters. The first chapter is introductory and contains the fundamental results of the theory of multifunctions and topological characteristics (topological degree and coincidence degree). The second chapter is devoted to the MGF and its modifications for solving various problems for differential inclusions in finite-dimensional spaces. The third chapter deals with the extension of the MGF to the case of differential inclusions in infinite-dimensional Hilbert spaces. In Chapter 4, by using the MGF, the authors obtain existence theorems for a boundary value problem for second-order differential inclusions in Hilbert spaces. The last chapter is devoted to the nonlinear Fredholm inclusions. The book is recommended for advanced graduate courses on nonlinear analysis.
scientific article; zbMATH DE number 6162125