Abstract
This chapter is devoted to the development of linear RFDEs, including the variation-of-constants formula, the formal adjoint of a linear system, and the relationship between the formal adjoint and the true adjoint. For an arbitrary two-point boundary-value problem, it is then shown there is a two-point boundary-value problem for the formal adjoint equation which fulfills the conditions for the usual Fredholm alternative. Also, relationships between various types of stability for linear systems are given.
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© 1977 Springer-Verlag New York Inc.
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Hale, J.K. (1977). General linear systems. In: Theory of Functional Differential Equations. Applied Mathematical Sciences, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9892-2_7
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DOI: https://doi.org/10.1007/978-1-4612-9892-2_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9894-6
Online ISBN: 978-1-4612-9892-2
eBook Packages: Springer Book Archive