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This book focuses on a large class of multi-valued variational
differential inequalities and inclusions of stationary and
evolutionary types with constraints reflected by subdifferentials
of convex functionals. Its main goal is to provide a systematic,
unified, and relatively self-contained exposition of existence,
comparison and enclosure principles, together with other
qualitative properties of multi-valued variational inequalities and
inclusions. The problems under consideration are studied in
different function spaces such as Sobolev spaces, Orlicz-Sobolev
spaces, Sobolev spaces with variable exponents, and Beppo-Levi
spaces. A general and comprehensive sub-supersolution method
(lattice method) is developed for both stationary and evolutionary
multi-valued variational inequalities, which preserves the
characteristic features of the commonly known sub-supersolution
method for single-valued, quasilinear elliptic and parabolic
problems. This method provides a powerful tool for studying
existence and enclosure properties of solutions when the coercivity
of the problems under consideration fails. It can also be used to
investigate qualitative properties such as the multiplicity and
location of solutions or the existence of extremal solutions. This
is the first in-depth treatise on the sub-supersolution (lattice)
method for multi-valued variational inequalities without any
variational structures, together with related topics. The choice of
the included materials and their organization in the book also
makes it useful and accessible to a large audience consisting of
graduate students and researchers in various areas of Mathematical
Analysis and Theoretical Physics.
This book focuses on a large class of multi-valued variational
differential inequalities and inclusions of stationary and
evolutionary types with constraints reflected by subdifferentials
of convex functionals. Its main goal is to provide a systematic,
unified, and relatively self-contained exposition of existence,
comparison and enclosure principles, together with other
qualitative properties of multi-valued variational inequalities and
inclusions. The problems under consideration are studied in
different function spaces such as Sobolev spaces, Orlicz-Sobolev
spaces, Sobolev spaces with variable exponents, and Beppo-Levi
spaces. A general and comprehensive sub-supersolution method
(lattice method) is developed for both stationary and evolutionary
multi-valued variational inequalities, which preserves the
characteristic features of the commonly known sub-supersolution
method for single-valued, quasilinear elliptic and parabolic
problems. This method provides a powerful tool for studying
existence and enclosure properties of solutions when the coercivity
of the problems under consideration fails. It can also be used to
investigate qualitative properties such as the multiplicity and
location of solutions or the existence of extremal solutions. This
is the first in-depth treatise on the sub-supersolution (lattice)
method for multi-valued variational inequalities without any
variational structures, together with related topics. The choice of
the included materials and their organization in the book also
makes it useful and accessible to a large audience consisting of
graduate students and researchers in various areas of Mathematical
Analysis and Theoretical Physics.
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.
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.
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