Boundedness properties for linear ordinary differential equations

Lovelady, David Lowell

doi:10.1090/S0002-9939-1973-0328202-7

Boundedness properties for linear ordinary differential equations
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Proc. Amer. Math. Soc. 41 (1973), 193-196 Request permission

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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