Nonlinear Differential Equations in Ordered Spaces: 1st Edition (Hardback) book cover

Nonlinear Differential Equations in Ordered Spaces

1st Edition

By S. Carl, Seppo Heikkila

Chapman and Hall/CRC

336 pages

Purchasing Options:$ = USD
Paperback: 9780367398477
pub: 2019-10-23
Hardback: 9781584880684
pub: 2000-06-14
eBook (VitalSource) : 9780429179617
pub: 2000-06-14
from $28.98

FREE Standard Shipping!


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.

Table of Contents

Operator Equations in Ordered Spaces and First Applications. Extremality Results for First Order Differential Equations. Uniqueness, Comparison and Well-Posedness Results for Quasilinear Differential Equations. Second Order Functional Differential Equations. Extremality Results for Quasilinear PDE. Differential Inclusions of Hemivariational Inequality Type. Discontinuous Implicit EIlliptic and Parabolic Problems. Appendix.

About the Authors

Carl, S.; Heikkila, Seppo

About the Series

Monographs and Surveys in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
SCIENCE / Mathematical Physics