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 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 monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.
Goethe's ranging literary genius, nimble yet luminous, resists simple classification. Poet and natural philosopher, critic and raconteur, Goethe was the most commanding literary presence of his time. Goethe and His Publishers organizes for the first time the myriad details of Goethe's career in print. Director of the German publishing company Suhrkamp Verlag, Siegfried Unseld brings a singular perspective to this biography, focusing our attention on an essential component of Goethe's literary endeavors: his relationship to his publishers. Carefully examining each work, Unseld covers the range of Goethe's oeuvre, from first anonymous publications to eventual monumental editions brought out by Johann Friedrich Cotta, the most renowned publisher of his day. Unseld sifts through the rich correspondence between Goethe and his publishers, as well as letters to and from friends, colleagues, and contemporaries. Analyzing publishing contracts, draft contracts, and historical documents, Unseld reveals the tremendous energy Goethe exerted on behalf of his manuscripts. During negotiations he was sometimes circumspect and reserved, other times demanding and assertive. These exchanges not only shed new light on Goethe's complex character but also show how he changed the author's role in the publishing process. Thus, this work offers a penetrating study on the intricate and many-tiered relations between author and publisher, then and today. Goethe and His Publishers celebrates Goethe's works, his life, and his times, from the viewpoint of a publisher today. Written by an individual who has devoted much of his life to the study of the poet whom he reveres, such a personal approach not only forms an excellent introduction to Goethe's work but helps restore Goethe to his rightful place in the world of letters.
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