Geodesic
Completeness of elementary solutions of second order elliptic equations in a semi-infinite tube domain
Electronic journal of differential equations, Tome 2002 (2002)
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.
Classification : 47E05, 35J25, 35P10
Keywords: abstract differential equations, second order elliptic equations, semi-infinite tube domains, isomorphism, completeness 
@article{EJDE_2002__2002__a39,
     author = {Yakubov,  Yakov},
     title = {Completeness of elementary solutions of second order elliptic equations in a semi-infinite tube domain},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1008.47044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a39/}
}
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Yakubov,  Yakov. Completeness of elementary solutions of second order elliptic equations in a semi-infinite tube domain. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a39/