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

Authors

  • Karwan H.F. Jwamer School of Science, University of Sulaimani, Kurdistan Region, Iraq. Author
  • Aryan Ali. M. School of Science, University of Sulaimani, Kurdistan Region, Iraq. Author

DOI:

https://doi.org/10.17656/jzs.10235

Keywords:

Spectral problem, Weight function, Lipschitz condition, Cauchy problem 2000 MR Subject Classification: 34B05, 34B15, 34L20

Abstract

In this paper we study the boundeness of the eigenfuctions of the spectral problem of the form:

-y” (x) + p(x) y’ (x) + q(x)y(x)= λp(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:

fun1.PNG   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].

References

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-Jwamer K.H.F, Analysis of Spectral characteristics of one nonself – adjoint problem withnon smooth coefficients, PhD thesis, Dagestan State University, 2010.

-JwamerK. H-F. and AigounovG. A. , About Uniform Limitation of Normalized Eigen Functions of T. Regge Problem in the Case of Weight Functions, Satisfying to Lipschitz Condition, Gen. Math. Notes, 1(2) (2010) 115-129.

-JwamerK. H-F. andQaderK. H., Estimates Normalized Eigenfunction to the BoundaryValue Problem in Different Cases of Weight Functions, Int. J. Open Problems Compt.Math., 4(3) (2011) 28-38.

-Naimark .M.A, Linear Differential Operators, New York, USA,1968.

-ShkalikovA.A,Boundaryvalue problem with a spectral parameter in the boundary conditions, Zeitchrift fur AngewandteMathematik und Mechanik, Vol.76, pp.133- 135,1996.

Published

2012-12-17

How to Cite

Boundedness of Normalized Eigenfunctions of the Spectral Problem in the Case of Weight Function Satisfying the Lipschitz Condition. (2012). Journal of Zankoy Sulaimani, 15(1), 79-94. https://doi.org/10.17656/jzs.10235