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 explic...
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| Format: | eBook |
| Language: | English |
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Boca Raton :
Chapman & Hall/CRC,
©2000.
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| Series: | Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ;
111. |
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| Online Access: | Connect to the full text of this electronic book |
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 quasilinear problems; 5.4. Notes and comments; 6. Differential inclusions of hemivariational inequality type; 6.1. Quasilinear elliptic inclusions with state-dependent subdifferentials; 6.2. State-dependent subdifferentials perturbed by discontinuous nonlinearities; 6.3. Elliptic inclusions with generalized gradients; 6.4. Quasilinear parabolic inclusions with state-dependent subdifferentials; 6.5. Notes and comments; 7. Discontinuous implicit elliptic and parabolic problems; 7.1. Statement of the problem and notations; 7.2. Preliminaries.
- 7.3. Main results7.4. Implicit elliptic problems; 7.5. Notes and comments; Appendix; A. Analysis in ordered spaces; B. Inequalities; C. Sobolev spaces; D. Pseudomonotone and quasilinear elliptic operators; E. Nonlinear first order evolution equations; F. Nonsmooth analysis; References; Index.