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Displaying similar documents to “Some properties of eigenfunctions of linear pencils and applications to mixed type operator-differential equations”

Spectral properties of some regular boundary value problems for fourth order differential operators

Nazim Kerimov, Ufuk Kaya (2013)

Open Mathematics

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In this paper we consider the problem y i v + p 2 ( x ) y ' ' + p 1 ( x ) y ' + p 0 ( x ) y = λ y , 0 < x < 1 , y ( s ) ( 1 ) - ( - 1 ) σ y ( s ) ( 0 ) + ∑ l = 0 s - 1 α s , l y ( l ) ( 0 ) = 0 , s = 1 , 2 , 3 , y ( 1 ) - ( - 1 ) σ y ( 0 ) = 0 , 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, l = 0 , s - 1 ¯ , 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...