### Abstract

Let L be an arbitrary linear partial differential operator and let f be an almost periodic function for t in R^{m}. 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 - Jan 1 1973 |

### Fingerprint

### Cite this

*Journal of Mathematical Analysis and Applications*,

*42*(2), 302-312. https://doi.org/10.1016/0022-247X(73)90139-X

**Almost periodic solutions of linear partial differential equations.** / Sell, George R.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 42, no. 2, pp. 302-312. https://doi.org/10.1016/0022-247X(73)90139-X

}

TY - JOUR

T1 - Almost periodic solutions of linear partial differential equations

AU - Sell, George R

PY - 1973/1/1

Y1 - 1973/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=49549167477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549167477&partnerID=8YFLogxK

U2 - 10.1016/0022-247X(73)90139-X

DO - 10.1016/0022-247X(73)90139-X

M3 - Article

VL - 42

SP - 302

EP - 312

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -