Some functional differential equations
Author:
Ll. G. Chambers
Journal:
Quart. Appl. Math. 32 (1975), 445-456
MSC:
Primary 34K10
DOI:
https://doi.org/10.1090/qam/481357
MathSciNet review:
481357
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Abstract: Sufficient conditions are given for the solution of the functional differential equations with associated boundary conditions \[ dy/dx = \sum \limits _{n = 0}^\infty {{a_n}y\left ( {{\mu ^n}x} \right ),\qquad y\left ( 0 \right ) = 1, \\ dy/dx = \int _0^\infty {a\left ( u \right )y\left ( {{\mu ^u}x} \right )du},\qquad y\left ( 0 \right ) = 1} \] A discussion is also given of some possible solutions to the differential equations which do not satisfy the boundary conditions.
G. Doetsch, Theorie und Anwendung der Laplace-Transformation, Springer, Berlin, 1937, 202
V. I. Smirnov, A course of higher mathematics IV, Pergamon, Oxford, 1964, 136
- L. Fox, D. F. Mayers, J. R. Ockendon, and A. B. Tayler, On a functional differential equation, J. Inst. Math. Appl. 8 (1971), 271–307. MR 301330
- Tosio Kato and J. B. McLeod, The functional-differential equation $y^{\prime } \,(x)=ay(\lambda x)+by(x)$, Bull. Amer. Math. Soc. 77 (1971), 891–937. MR 283338, DOI https://doi.org/10.1090/S0002-9904-1971-12805-7
G. Doetsch, Theorie und Anwendung der Laplace-Transformation, Springer, Berlin, 1937, 202
V. I. Smirnov, A course of higher mathematics IV, Pergamon, Oxford, 1964, 136
L. Fox, D. F. Mayers, J. R. Ockendon and A. B. Tayler, J. Inst. Maths. Applics. 8, 271 (1971)
T. Kato and J. B. Mcleod, Bull. Amer. Math. Soc. 77, (1971) 891
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© Copyright 1975
American Mathematical Society