JIPAM logo: Home Link
Home Editors Submissions Reviews Volumes RGMIA About Us

  Volume 8, Issue 4, Article 107
Some Precise Estimates of the Hyper Order of Solutions of Some Complex Linear Differential Equations

    Authors: Benharrat Belaidi,  
    Date Received: 05/03/07  
    Date Accepted: 30/11/07  
    Subject Codes:

34M10, 30D35.

    Editors: Doru Stefanescu,  

Let $ rho left( fright) $ and $ rho _{2}left( fright) $ denote respectively the order and the hyper order of an entire function$  f.$ In this paper, we obtain some precise estimates of the hyper order of solutions of the following higher order linear differential equations

$displaystyle f^{left( kright) }+sum_{j=0}^{k-1}A_{j}left( zright) e^{P_{j}left( zright) }f^{left( jright) }=0$

$displaystyle f^{left( kright) }+sum_{j=0}^{k-1}left( A_{j}left( zright) e^{P_{j}left( zright) }+B_{j}left( zright) right) f^{left( jright) }=0$

where $ kgeq 2,$ $ P_{j}left( zright) $ $ left( j=0,dots ,k-1right) $ are nonconstant polynomials such that $ deg P_{j}=n$ $ left( j=0,dots ,k-1right) $ and $ A_{j}left( zright) $ $ left( notequiv 0right) ,$ $ B_{j}left( zright) $ $ left( notequiv 0right) $ $ left( j=0,dots ,k-1right) $ are entire functions with $ left( j=0,dots ,k-1right) $. Under some conditions, we prove that every solution $ fleft( zright) notequiv 0$ of the above equations is of infinite order and $ rho _{2}left( fright) =n$.

  Download Screen PDF
  Download Print PDF
  Send this article to a friend
  Print this page

      search [advanced search] copyright 2003 terms and conditions login