Abstract
Let L be an arbitrary linear partial differential operator and let f be an almost periodic function for t in Rm. In this paper we present sufficient conditions that a bounded solution u of Lu = f be almost periodic. Our work generalizes the theorem of Sibuya [5] for Poisson's equation and the theorems of Favard [3] and Bochner [1] for ordinary differential equations.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 302-312 |
| Number of pages | 11 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 42 |
| Issue number | 2 |
| DOIs | |
| State | Published - May 1973 |
Bibliographical note
Funding Information:* This work was done while the author was visiting the Istituto Matematico dell’Universit8 di Firenze under the auspices of the Italian Research Council (C.N.R.). Partial support for this research was also given by NSF Grant No. GP-27275.