Nonlinear differential equations in ordered spaces
"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 im…
Read More ↓Title Statements
- Full title :Nonlinear differential equations in ordered spaces / S. Carl, S. Heikkilä.
Summary
"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."--Provided by publisher.
Read More ↓Edition Statements
- Publication Date:©2000.
Publication Statements
- Publisher(s):Chapman & Hall/CRC
- Place of Publication:Boca Raton
- Language:eng
- Publication Date:©2000.
The Physical Object
- Description:1 online resource.
Edition Identifiers
- ISBN:9781482280951, 1482280957, 9781420026160, 142002616X
- DOI:10.1201/9781482280951
- oclc:on1021305692
- LC Classification:QA372
- Dewey Decimal:515.355
Table of Contents
Cover; Title Page; Copyright Page; Table of Contents; Introduction; 1. Operator equations in ordered spaces and first applications; 1.1. Operator equations in ordered spaces; 1.2. Applications to differential equations; 1.3. Notes and comments; 2. Extremality results for first order differential equations; 2.1. Explicit initial value problems; 2.2. Explicit boundary value problems; 2.3. Explicit functional problems; 2.4. Implicit functional problems; 2.5. Notes and comments; 3. Uniqueness, comparison, and well-posedness results for quasilinear differential equations.
3.1. First order boundary value problems3.2. First order initial value problems; 3.3. Well-posedness results; 3.4. Second order problems; 3.5. Notes and comments; 4. Second order functional differential equations; 4.1. Explicit Sturm-Liouville boundary value problems; 4.2. Implicit Sturm-Liouville boundary value problems; 4.3. Convergence of successive approximations; 4.4. Explicit phi-Laplacian problems; 4.5. Implicit phi-Laplacian problems; 4.6. Notes and comments; 5. Extremality results for quasilinear PDE; 5.1. Quasilinear elliptic boundary value problems.
5.2. Quasilinear parabolic problems5.3. Discontinuous qu…
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