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This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for "pure" mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.

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1 Background.- 2 MGF in Finite-Dimensional Spaces.- 3 Guiding Functions in Hilbert Spaces.- 4 Second-Order Differential Inclusions.- 5 Nonlinear Fredholm Inclusions.

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From the reviews:

"The central topic of this volume is the theory of guiding functions methods ... . The book also collects all the related results achieved by the authors in their papers in the last 10 years. ... a high-quality piece of work on the advanced theory of multimaps, and it can be quite useful and readable for graduate students and researchers in this field." (Arsen Palestini, Mathematical Reviews, February, 2014)

"The monograph under review concerns the method of guiding functions (MGF) for solving problems of periodic oscillations in nonlinear systems. ... The book is recommended for advanced graduate courses on nonlinear analysis." (Ovidiu Cârja, zbMATH, Vol. 1282, 2014)

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