Boundedness of Normalized Eigenfunctions of the Spectral Problem in the Case of Weight Function Satisfying the Lipschitz Condition

Volume 15 , Issue 1 , December 2013 , Pages 79-94

Authors

¹ School of Science, University of Sulaimani

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].

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