SPECTRAL PROPERTIES OF SCHRODINGER OPERATOR WITH A GENERAL BOUNDARY CONDITIONS ON FINITE TIME SCALE

Year 2016, Volume: 29 Issue: 2, 467 - 472, 21.06.2016

Esra Kır Arpat Hatice Terzi

Abstract

In this paper we consider the operator L generated in 𝐿∇2 [𝑎, 𝑏] by the boundary problem−[𝑦∆(𝑡)]∇ + [𝜆 + 𝑞(𝑡)]2𝑦(𝑡) = 0, 𝑡 ∈ [𝑎, 𝑏],𝑦(𝑎) − 𝑘𝑦∆(𝑎) = 0, 𝑦(𝑏) + 𝐾𝑦∆(𝑏) = 0 where 𝑞(𝑡) is partial continuous, 𝑞(𝑡) ≥ 0, 𝑘 ≥ 0,𝐾 ≥ 0. In this paper, spectral properties of Schrodinger problem on finite time scale is examined and the formula of convergent expansion is obtained which is form of series in terms of the eigenfunctions in 𝐿∇2 [𝑎, 𝑏] space.

Keywords

Time scale, delta and nabla derivatives, Schrödinger operator, eigenvalue, eigenfunction.

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