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

Authors : Serdar PAŞ, Kadriye AYDEMİR, Fahreddin MUHTAROV

Pages : 40-49

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Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :This work is concerned with the boundary-value-transition problem consisting of a two-interval Sturm-Liouville equation Lu ≔ −u′′insert ignore into journalissuearticles values(x); + qinsert ignore into journalissuearticles values(x);uinsert ignore into journalissuearticles values(x); = λuinsert ignore into journalissuearticles values(x); , x ∈ [−1,0); ∪ insert ignore into journalissuearticles values(0,1] together with anti-periodic boundary conditions, given by uinsert ignore into journalissuearticles values(−1); = −uinsert ignore into journalissuearticles values(1); u′insert ignore into journalissuearticles values(−1); = −u′insert ignore into journalissuearticles values(1); and transition conditions at the interior point x = 0, given by uinsert ignore into journalissuearticles values(+0); = Kuinsert ignore into journalissuearticles values(−0); u′insert ignore into journalissuearticles values(+0); =1/Ku′insert ignore into journalissuearticles values(−0); where qinsert ignore into journalissuearticles values(x); is a continuous function in the intervals [−1,0); and insert ignore into journalissuearticles values(0,1] with finite limit values qinsert ignore into journalissuearticles values(±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