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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Boundedness properties for linear ordinary differential equations


Author: David Lowell Lovelady
Journal: Proc. Amer. Math. Soc. 41 (1973), 193-196
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1973-0328202-7
MathSciNet review: 0328202
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Abstract: In comparing a linear equation and the associated nonhomogeneous equation, it is shown that if every bounded forcing function and every $ {\mathcal{L}^1}$ forcing function yields at least one bounded solution, then the bounded subset of the solution family of the homogeneous equation is uniformly ultimately bounded.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0328202-7
Keywords: Uniform boundedness, uniform ultimate boundedness, evolution systems
Article copyright: © Copyright 1973 American Mathematical Society