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# On solutions of parabolic and elliptic type differential equations on $(-\infty, \infty)$ in a Banach space

### Abstract

We show that every classical solution of a parabolic or elliptic type homogeneous differential equation on $(-\infty, \infty)$ in a Banach space may be extended to an entire vector-valued function. The description of all the solutions is given, and necessary and sufficient conditions for a solution to be continued to a finite order and finite type entire vector-valued function are presented.

### Article Information

 Title On solutions of parabolic and elliptic type differential equations on $(-\infty, \infty)$ in a Banach space Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 2, 177-183 MathSciNet MR2432766 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

Volodymyr M. Gorbachuk
National Technical University "KPI", 37 Peremogy Prosp., Kyiv, 06256, Ukraine

### Citation Example

Volodymyr M. Gorbachuk, On solutions of parabolic and elliptic type differential equations on $(-\infty, \infty)$ in a Banach space, Methods Funct. Anal. Topology 14 (2008), no. 2, 177-183.

### BibTex

@article {MFAT463,
AUTHOR = {Gorbachuk, Volodymyr M.},
TITLE = {On solutions of parabolic and elliptic type differential equations on $(-\infty, \infty)$ in a Banach space},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {2},
PAGES = {177-183},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=463},
}