Electron. J. Diff. Eqns., Vol. 2002(2002), No. 03, pp. 1-21.

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

Yakov Yakubov

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.

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Yakov Yakubov
Raymond and Beverly Sackler Faculty of Exact Sciences
School of Mathematical Sciences, Tel-Aviv University
Ramat-Aviv 69978, Israel
e-mail: yakubov@post.tau.ac.il

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