In this paper we consider the problem where λ is a spectral parameter; p j (x) ∈ L 1(0, 1), j = 0, 1, 2, are complex-valued functions; α s;l, s = 1, 2, 3, , are arbitrary complex constants; and σ = 0, 1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established in the case α 3,2 + α 1,0 ≠ α 2,1. It is proved that the system of root functions of this spectral problem forms a basis in the space L p(0, 1), 1 < p < ∞, when α 3,2+α 1,0 ≠ α 2,1, p j (x) ∈ W 1j(0, 1), j = 1, 2, and p 0(x) ∈ L 1(0, 1); moreover, this basis is unconditional for p = 2.
@article{bwmeta1.element.doi-10_2478_s11533-012-0059-x,
author = {Nazim Kerimov and Ufuk Kaya},
title = {Spectral properties of some regular boundary value problems for fourth order differential operators},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {94-111},
zbl = {1272.34025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0059-x}
}
Nazim Kerimov; Ufuk Kaya. Spectral properties of some regular boundary value problems for fourth order differential operators. Open Mathematics, Tome 11 (2013) pp. 94-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0059-x/
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