Abstract
We are concerned with the almost automorphic solutions to the second-order hyperbolic differential equations of type ü(s) + 2B ù(s) + Au(s) = f(s) (*), where A, B are densely defined closed linear operators acting in a Hilbert space H, and f : R |—> H is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions, every solution to (*) is almost automorphic.
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Edited by Jerome A. Goldstein
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Diagana, T. Some Remarks on Some Second-order Hyperbolic Differential Equations. Semigroup Forum 68, 357–364 (2004). https://doi.org/10.1007/s00233-003-0016-x
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DOI: https://doi.org/10.1007/s00233-003-0016-x