Nonlinear Differential Equations in Ordered Spaces (Monographs and Surveys in Pure and Applied Mathematics) - Hardcover

Carl, S.; Heikkila, Seppo

Hardcover

ISBN 10: 1584880686 ISBN 13: 9781584880684

Publisher: Chapman and Hall/CRC, 2000

Synopsis

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.

About this title

About the Author

Carl, S.; Heikkila, Seppo

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2000
• Language: English
• ISBN 10: 1584880686
• ISBN 13: 9781584880684
• Binding: Hardcover
• Edition number: 1
• Number of pages: 336