Applied Theory of Functional Differential Equations

Inhaltsverzeichnis

• 1. Models.
• 1. Formal prerequisites.
• 2. Aftereffect in mechanics.
• 3. Hereditary phenomena in physics.
• 4. Models with delays in technical problems.
• 5. Aftereffect in biology.
• 6. Aftereffect in medicine.
• 7. Aftereffect in economy and other sciences.
• 2. General theory.
• 1. Introduction. Method of steps.
• 2. Cauchy problem for RDEs.
• 3. Cauchy problem for NDEs.
• 4. Differential inclusions of retarded type (RDIs).
• 5. General linear equations with aftereffect.
• 6. Linear autonomous equations.
• 7. Hopf bifurcation.
• 8. Stocnastic retarded differential equations (SRDEs).
• 3. Stability of retarded differential equations.
• 1. Liapunov’s direct method.
• 2. Linear autonomous equations.
• 4. Stability of neutral type functional differential equations.
• 1. Direct Liapunov’s method.
• 2. Stability of linear autonomous equations.
• 5. Stability of stochastic functional differential equations.
• 1. Statement of the problem.
• 2. Liapunov’s direct method.
• 3. Boundedness of moments of solutions.
• 6. Problems of control for deterministic FDEs.
• 1. The dynamic programming method for deterministic equations. Bellman’s equation.
• 2. Linear quadratic problems.
• 3. Optimal control of bilinear hereditary systems.
• 4. Control problems with phase constraint formula.
• 5. Necessary optimality conditions.
• 7. Optimal control of stochastic delay systems.
• 1. Dynamic programming method for controlled stochastic hereditary processes.
• 2. The linear quadratic problem.
• 3. Approximate optimal control for systems with small parameters.
• 4. Another approach to the problem of optimal synthesis control.
• 8. State estimates of stochastic systems with delay.
• 1. Filtering of Gaussian processes.
• 2. Filtering of solutions of Itô equations with delay.