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Square integrable solutions of $ Ly=f(t,\,y)$


Author: Anton Zettl
Journal: Proc. Amer. Math. Soc. 26 (1970), 635-639
MSC: Primary 34.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0267213-4
MathSciNet review: 0267213
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Abstract: Let $ L$ be an ordinary linear differential operator and $ {L^ + }$ its formal adjoint. It is shown that, under suitable conditions on $ f$, all solutions of $ Ly = f(t,y)$ are in $ {L^2}(0,\infty )$ provided that all those of $ Ly = 0$ and $ {L^ + }y = 0$ are.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0267213-4
Keywords: Square integrable solutions, differential operators, Gronwall inequality, variation of parameters
Article copyright: © Copyright 1970 American Mathematical Society

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