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Extremality results proved in this Monograph for an abstract
operator equation provide the theoretical framework for developing
new methods that allow the treatment of a variety of discontinuous
initial and boundary value problems for both ordinary and partial
differential equations, in explicit and implicit forms. By means of
these extremality results, the authors prove the existence of
extremal solutions between appropriate upper and lower solutions of
first and second order discontinuous implicit and explicit ordinary
and functional differential equations. They then study the
dependence of these extremal solutions on the data. The authors
begin by developing an existence theory for an abstract operator
equation in ordered spaces and offer new tools for dealing with
different kinds of discontinuous implicit and explicit differential
equation problems. They present a unified approach to the existence
of extremal solutions of quasilinear elliptic and parabolic
problems and extend the upper and lower solution method to elliptic
and parabolic inclusion of hemivariation type using variational and
nonvariational methods. Nonlinear Differential Equations in Ordered
Spaces includes research that appears for the first time in book
form and is designed as a source book for pure and applied
mathematicians. Its self-contained presentation along with numerous
worked examples and complete, detailed proofs also make it
accessible to researchers in engineering as well as advanced
students in these fields.
Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. By means of these extremality results, the authors prove the existence of extremal solutions between appropriate upper and lower solutions of first and second order discontinuous implicit and explicit ordinary and functional differential equations. They then study the dependence of these extremal solutions on the data.
The authors begin by developing an existence theory for an abstract operator equation in ordered spaces and offer new tools for dealing with different kinds of discontinuous implicit and explicit differential equation problems. They present a unified approach to the existence of extremal solutions of quasilinear elliptic and parabolic problems and extend the upper and lower solution method to elliptic and parabolic inclusion of hemivariation type using variational and nonvariational methods.
Nonlinear Differential Equations in Ordered Spaces includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. Its self-contained presentation along with numerous worked examples and complete, detailed proofs also make it accessible to researchers in engineering as well as advanced students in these fields.
This monograph provides a unified and comprehensive treatment of an
order-theoretic fixed point theory in partially ordered sets and
its various useful interactions with topological structures. The
material progresses systematically, by presenting the preliminaries
before moving to more advanced topics. In the treatment of the
applications a wide range of mathematical theories and methods from
nonlinear analysis and integration theory are applied; an outline
of which has been given an appendix chapter to make the book
self-contained. Graduate students and researchers in nonlinear
analysis, pure and applied mathematics, game theory and
mathematical economics will find this book useful.
This monograph provides a unified and comprehensive treatment of an
order-theoretic fixed point theory in partially ordered sets and
its various useful interactions with topological structures. The
material progresses systematically, by presenting the preliminaries
before moving to more advanced topics. In the treatment of the
applications a wide range of mathematical theories and methods from
nonlinear analysis and integration theory are applied; an outline
of which has been given an appendix chapter to make the book
self-contained. Graduate students and researchers in nonlinear
analysis, pure and applied mathematics, game theory and
mathematical economics will find this book useful.
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