Vy Khoi Le Knihy

Focusing on bifurcation theory for variational inequalities in reflexive spaces, this book provides a comprehensive overview and its applications in various fields, including elasticity theory, fluid mechanics, and quasilinear elliptic partial differential equations. It employs modern nonlinear analysis techniques, making it suitable for graduate students and researchers in nonlinear analysis and related disciplines. The text aims to bridge theoretical concepts with practical applications, enhancing understanding in both academic and research settings.

The book delves into multi-valued variational differential inequalities and inclusions, both stationary and evolutionary, emphasizing the role of convex functional subdifferentials. It aims to present a cohesive and self-sufficient exploration of existence, comparison, and enclosure principles, alongside other qualitative attributes of these inequalities. The study spans various function spaces, including Sobolev, Orlicz-Sobolev, and Beppo-Levi spaces, providing a comprehensive framework for understanding these complex mathematical concepts.

The book delves into nonsmooth variational problems related to boundary value issues characterized by nonsmooth data and constraints. It covers a range of topics, including multivalued elliptic problems, variational inequalities, and hemivariational inequalities, along with their evolution problems. This specialized exploration highlights the complexities and mathematical intricacies involved in these types of variational challenges.

An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and quasilinear elliptic partial differential equations. The tools employed are those of modern nonlinear analysis. Accessible to graduate students and researchers who work in nonlinear analysis, nonlinear partial differential equations, and additional research disciplines that use nonlinear mathematics.