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On The Spectral Properties Of The Regular Sturm-Liouville Problem With The Lag Argument For Which Its Boundary Conditions Depends On The Spectral Parameter, Mehmet Bayramoğlu, Kevser Özden Köklü, Oya Baykal
On The Spectral Properties Of The Regular Sturm-Liouville Problem With The Lag Argument For Which Its Boundary Conditions Depends On The Spectral Parameter, Mehmet Bayramoğlu, Kevser Özden Köklü, Oya Baykal
Turkish Journal of Mathematics
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.