Boundedness of Normalized Eigenfunctions of the Spectral Problem in the Case of Weight Function Satisfying the Lipschitz Condition - Jwamer, Karwan H.F.; M, Aryan Ali. (Sulaimani Journal for Pure and Applied Sciences, 2013)
In this paper we study the boundeness of the eigenfuctions of the spectral problem of the form: -y” (x) + p1 (x) y’ (x) + q1 (x)y(x)= λ2 p(x)y(x), x∈(0,a) (1) With the boundary conditions: y(0) = 0, y’ (a) - i λy(a)=0, (2) and the normalized condition: where λ is spectral parameter and p(x) is a wight function satisfy Lipschitz condition, that is ( p(x) ∈ Lip1) /p(x2) – p(x1) | ≤ k | x2 – x1 | , ∀ x1, x2 ∈ [0, a], k is Lipschitz constant, and p1 (x) ≠ 0, p1 (x) ∈ C1 [0,a], q1 (x) ∈ C[0,a].
Keywords: Spectral problem; weight function; Lipschitz condition; Cauchy problem 2000 MR Subject Classification 34B05; 34B15; 34L20