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

Bayram E., Cebesoy S., Erdal İ.

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, cilt.9, sa.4, ss.1454-1469, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.11948/2156-907x.20180280
  • Dergi Adı: JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1454-1469
  • Anahtar Kelimeler: Asymptotic, eigenvalues, impulsive conditions, quadratic pencil of difference equations, resolvent operator, spectral singularities, spectrum, SCHRODINGER-OPERATORS, EQUATIONS, 2ND-ORDER
  • Ankara Üniversitesi Adresli: Evet

Özet

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.