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.

Full Text

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},
  MRNUMBER = {MR2432766},
       URL = {http://mfat.imath.kiev.ua/article/?id=463},
}