Geodesic
Completeness Theorem for Singular Differential Pencils
Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 558-576

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A theorem completeness theorem of special vector functions induced by the products of the so-called Weyl solutions of a fourth-order differential equation and by their derivatives on the semiaxis is presented. We prove that such nonlinear combinations of Weyl solutions and their derivatives constitute a linear subspace of decreasing (at infinity) solutions of a linear singular differential system of Kamke type. We construct and study the Green function of the corresponding singular boundary-value problems on the semiaxis for operator pencils defining differential systems of Kamke type. The required completeness theorem is proved by using the analytic and asymptotic properties of the Green function, operator spectral theory methods, and analytic function theory.
Keywords: singular differential pencil, fourth-order differential equation, Green function, boundary-value problem, operator spectral theory.
Mots-clés : Weyl solution 
@article{MZM_2011_89_4_a7,
     author = {D. V. Poplavsky},
     title = {Completeness {Theorem} for {Singular} {Differential} {Pencils}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {558--576},
     publisher = {mathdoc},
     volume = {89},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a7/}
}
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D. V. Poplavsky. Completeness Theorem for Singular Differential Pencils. Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 558-576. http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a7/