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The spectrum of eigenparameter-dependent discrete Sturm–Liouville equations

✍ Scribed by Elgiz Bairamov; Yelda Aygar; Turhan Koprubasi

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
225 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

Let us consider the boundary value problem (BVP) for the discrete Sturm-Liouville equation

where (a n ) and (b n ), n ∈ N are complex sequences, γ i , β i ∈ C, i = 0, 1, and λ is a eigenparameter. Discussing the point spectrum, we prove that the BVP (0.1), (0.2) has a finite number of eigenvalues and spectral singularities with a finite multiplicities, if

for some ε > 0 and 1 2 ≤ δ ≤ 1.

📜 SIMILAR VOLUMES

Weight Summability of Solutions of the S
Weight Summability of Solutions of the Sturm–Liouville Equation
✍ N Chernyavskaya; L Shuster 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 154 KB

We consider an equation &y"(x)+q(x) y(x)=f (x), x # R; ( 1 ) We study requirements for a weight function r(x) # L loc p (R) and for q(x) under which, for a given p # [1, ], regardless of f (x) # L p (R), the solution y(x) # L p (R) of Eq. (1) satisfies the inequalities: