Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems

Year 2020, Issue: 33, 40 - 49, 31.12.2020

Serdar Paş , Kadriye Aydemir , Fahreddin Muhtarov

Abstract

This work is concerned with the boundary-value-transition problem consisting of a
two-interval Sturm-Liouville equation
Lu ≔ −u′′(x) + q(x)u(x) = λu(x) , x ∈ [−1,0) ∪ (0,1]

together with anti-periodic boundary conditions, given by
u(−1) = −u(1)
u′(−1) = −u′(1)
and transition conditions at the interior point x = 0, given by
u(+0) = Ku(−0)
u′(+0) =1/Ku′(−0)

where q(x) is a continuous function in the intervals [−1,0) and (0,1] with finite limit values q(±0) ,
K ≠ 0 is the real number and λ is the complex eigenvalue parameter. In this study we shall investigate
some properties of the eigenvalues and eigenfunctions of the considered problem.

Keywords

Anti-periodic Sturm-Liouville problem,, eigenvalue,, eigenfunction,, transition condition

Project Number

FMB-BAP 19-0391.

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