PROPERTIES OF EIGENVALUES AND SPECTRAL SINGULARITIES FOR IMPULSIVE QUADRATIC PENCIL OF DIFFERENCE OPERATORS

Elgiz Bairamov; Serifenur Cebesoy; Ibrahim Erdal

doi:10.11948/2156-907X.20180280

2019 Volume 9 Issue 4

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Elgiz Bairamov, Serifenur Cebesoy, Ibrahim Erdal. PROPERTIES OF EIGENVALUES AND SPECTRAL SINGULARITIES FOR IMPULSIVE QUADRATIC PENCIL OF DIFFERENCE OPERATORS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1454-1469. doi: 10.11948/2156-907X.20180280

Citation:

Elgiz Bairamov, Serifenur Cebesoy, Ibrahim Erdal. PROPERTIES OF EIGENVALUES AND SPECTRAL SINGULARITIES FOR IMPULSIVE QUADRATIC PENCIL OF DIFFERENCE OPERATORS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1454-1469. doi: 10.11948/2156-907X.20180280

PROPERTIES OF EIGENVALUES AND SPECTRAL SINGULARITIES FOR IMPULSIVE QUADRATIC PENCIL OF DIFFERENCE OPERATORS

1.
Ankara University, Faculty of Science, Department of Mathematics, 06100 Ankara, Turkey
2.
Çankırı Karatekin University, Faculty of Science, Department of Mathematics, 18200 Çankırı, Turkey

Corresponding author: Email address:scebesoy@karatekin.edu.tr(S. Cebesoy)

Abstract

Abstract

In this paper, we investigate the spectral analysis of impulsive quadratic pencil of difference operators. We first present a boundary value problem consisting one interior impulsive point on the whole axis corresponding to the above mentioned operator. After introducing the solutions of impulsive quadratic pencil of difference equation, we obtain the asymptotic equation of the function related to the Wronskian of these solutions to be helpful for further works, then we determine resolvent operator and continuous spectrum. Finally, we provide sufficient conditions guarenteeing finiteness of eigenvalues and spectral singularities by means of uniqueness theorems of analytic functions. The main aim of this paper is demonstrating the impulsive quadratic pencil of difference operator is of finite number of eigenvalues and spectral singularities with finite multiplicities which is an uninvestigated problem proposed in the literature.
- Asymptotic /
- eigenvalues /
- impulsive conditions /
- quadratic pencil of difference equations /
- resolvent operator /
- spectral singularities /
- spectrum
MSC: 39A10, 39A13, 47B39, 58C40

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References

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