Turkish Journal of Mathematics
DOI
-
Abstract
In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y''(t) + \lambda^2 y(t) + M(t)y (t - \Delta(t)) = 0 and the spectral parameter in the boundary conditions \lambda y(0) +y'(0) = 0 \lambda^{2}y(\pi) + y'(\pi) = 0 y(t - \Delta(t)) = y(0)\varphi(t - \Delta(t)), t - \Delta(t) < 0 has been founded in a finite interval, where M(t) and \Delta(t) \geq 0 are continuous functions on [0, \pi], \lambda > 0 is a real parameter, \varphi(t) is an initial function which is satisfied with the condition \varphi(0) = 1 and continuous in the initial set.
Keywords
Lag argument, Eigenvalue, Eigenfunction, Asymptotic expression.
First Page
421
Last Page
432
Recommended Citation
BAYRAMOĞLU, MEHMET; KÖKLÜ, KEVSER ÖZDEN; and BAYKAL, OYA (2002) "On the Spectral Properties of the Regular Sturm-Liouville Problem with the Lag Argument for Which its Boundary Conditions Depends on the Spectral Parameter," Turkish Journal of Mathematics: Vol. 26: No. 4, Article 4. Available at: https://journals.tubitak.gov.tr/math/vol26/iss4/4
