On the Spectral Properties of the Regular Sturm-Liouville Problem with the Lag Argument for Which its Boundary Conditions Depends on the Spectral Parameter

Authors : Mehmet BAYRAMOĞLU, Kevser ÖZDEN KÖKLÜ

Pages : 421-432

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y``insert ignore into journalissuearticles values(t); + l2 yinsert ignore into journalissuearticles values(t); + Minsert ignore into journalissuearticles values(t);y insert ignore into journalissuearticles values(t - Dinsert ignore into journalissuearticles values(t);); = 0 and the spectral parameter in the boundary conditions l yinsert ignore into journalissuearticles values(0); +y`insert ignore into journalissuearticles values(0); = 0 l2yinsert ignore into journalissuearticles values(p); + y`insert ignore into journalissuearticles values(p); = 0 yinsert ignore into journalissuearticles values(t - Dinsert ignore into journalissuearticles values(t);); = yinsert ignore into journalissuearticles values(0);jinsert ignore into journalissuearticles values(t - Dinsert ignore into journalissuearticles values(t););, t - Dinsert ignore into journalissuearticles values(t); < 0 has been founded in a finite interval, where Minsert ignore into journalissuearticles values(t); and Dinsert ignore into journalissuearticles values(t); \geq 0 are continuous functions on [0, p], l > 0 is a real parameter, jinsert ignore into journalissuearticles values(t); is an initial function which is satisfied with the condition jinsert ignore into journalissuearticles values(0); = 1 and continuous in the initial set.
Keywords : Lag argument, Eigenvalue, Eigenfunction, Asymptotic expression