Completeness of elementary solutions of second order elliptic equations in a semi-infinite tube domain

• Main Author: Yakov Yakubov
• Format: Article
• Language: English
• Published: Texas State University 2002-01-01
• Series: Electronic Journal of Differential Equations
• Subjects: Abstract differential equations; second order elliptic equations; semi-infinite tube domains; isomorphism; completeness.
• Online Access: http://ejde.math.txstate.edu/Volumes/2002/03/abstr.html

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.