Almost periodic solutions of linear partial differential equations

George R. Sell

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish (US)
Pages (from-to)302-312
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - May 1973
Externally publishedYes

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.


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