Abstract
The basic result of this chapter is formulated in Theorems 4.3 and 4.4 on the existence and continuous dependence of solutions of differential equations on the initial data and right-hand sides. These theorems are formulated and proved in Sections 4.4 and 4.5, and they appear as comparatively easy corollaries of Theorem 4.2 on the existence and continuous dependence of solutions of differential equations with fixed right-hand sides, which is proved in Section 4.3. The technique used for deriving Theorems 4.3 and 4.4 from Theorem 4.2 is standard, and it often turns out to be very useful.
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© 1978 Plenum Press, New York
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Gamkrelidze, R.V. (1978). The Existence and Continuous Dependence Theorem for Solutions of Differential Equations. In: Principles of Optimal Control Theory. Mathematical Concepts and Methods in Science and Engineering, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7398-8_4
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DOI: https://doi.org/10.1007/978-1-4684-7398-8_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-7400-8
Online ISBN: 978-1-4684-7398-8
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