Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 03, pp. 1-21.

Title: Completeness of elementary solutions of second order
       elliptic equations in a semi-infinite tube domain
   
Author: Yakov Yakubov (Tel-Aviv University, Israel)

Abstract:  
  Boundary-value problems for second order abstract differential
  equations on a semi-axis are considered in this article. 
  We find isomorphisms for the corresponding operators and 
  prove completeness of elementary solutions corresponding to 
  subsets of eigenvalues. As an application of the abstract results,
  we study second order elliptic equations in semi-infinite tube domains. 
  Our results can be applied to pure differential, integro-differential,
  functional-differential and equations with a shift.

Submitted October 29, 2001. Published January 2, 2002.
Math Subject Classifications:  47E05, 35J25, 35P10.
Key Words: Abstract differential equations; second order elliptic
    equations; semi-infinite tube domains; isomorphism; completeness.