Introduction to the theory of functional differential equations and their applications. Group approach |
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Authors: | Levon Andreevich Beklaryan |
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Institution: | (1) Central Economics and Mathematics Institute of the Russian Academy of Science, Russia |
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Abstract: | In this work, we give an introduction to the theory of nonlinear functional differential equations of pointwise type on a
finite interval, semi-axis, or axis. This approach is based on the formalism using group peculiarities of such differential
equations. For the main boundary-value problem and the Euler-Lagrange boundary-value problem, we consider the existence and
uniqueness of the solution, the continuous dependence of the solution on boundary-value and initial-value conditions, and
the “roughness” of functional differential equations in the considered boundary-value problems. For functional differential
equations of pointwise type we also investigate the pointwise completeness of the space of solutions for given boundary-value
conditions, give an estimate of the rank for the space of solutions, describe types of degeneration for the space of solutions,
and establish conditions for the “smoothness” of the solution. We propose the method of regular extension of the class of
ordinary differential equations in the class of functional differential equations of pointwise type.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 8, Functional Differential Equations, 2004. |
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Keywords: | |
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