The Continuous Maximum Principle
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An Introduction to Maximum Principles and Symmetry in Elliptic Problems
Author: L. E. Fraenkel
language: en
Publisher: Cambridge University Press
Release Date: 2000-02-25
Advanced text, originally published in 2000, on differential equations, with plentiful supply of exercises all with detailed hints.
Optimal Control of Nonlinear Processes
Author: Dieter Grass
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-07-24
Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site.
Maximum Principles for the Hill's Equation
Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,...) and for problems with parametric dependence. The authors discuss the properties of the related Green's functions coupled with different boundary value conditions. In addition, they establish the equations' relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included. - Evaluates classical topics in the Hill's equation that are crucial for understanding modern physical models and non-linear applications - Describes explicit and effective conditions on maximum and anti-maximum principles - Collates information from disparate sources in one self-contained volume, with extensive referencing throughout