MULTIFUNCTIONS, MINIMA AND MINIMAX WITH SELECTED APPLICATIONS

This comprehensive research monograph offers a unified and in-depth account of Biagio Ricceri's groundbreaking contributions over the past 45 years in variational analysis, critical point theory, optimization, and nonlinear analysis.Organically structured, the book presents a reasoned overview of foundational results such as Ricceri's variational principle, Ricceri's minimax theorems, and Ricceri's three critical points theorems — which have become widely used tools for proving the existence and multiplicity of solutions in nonlinear differential equations and variational problems.Going beyond personal contributions, the book also examines how Ricceri's ideas have inspired further developments by other researchers, with a special focus on applications across functional analysis, optimization without convexity, differential equations, fixed point theory, and control theory.Key theoretical tools are presented alongside their applications to boundary value problems, nonlocal problems, and nonsmooth variational frameworks, offering direct insight into the mathematical mechanisms from the originator himself.This book is essential reading for graduate students, researchers, and specialists in mathematical analysis, variational methods, applied mathematics, and nonlinear PDEs, particularly those seeking authoritative guidance in applying abstract variational principles to concrete problems.