Abstract
In this study, a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition and with transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. MSC (2010): 34L20; 35R10.
Highlights
We study the eigenvalues and eigenfunctions of discontinuous boundary-value problem with retarded argument and a spectral parameter in the boundary condition
4 Conclusion In this study, first, we obtain asymptotic formulas for eigenvalues and eigenfunctions for discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition
Under additional conditions (a) and (b) the more exact asymptotic formulas, which depend upon the retardation obtained
Summary
Boundary-value problems for differential equations of the second order with retarded argument were studied in [1,2,3,4,5], and various physical applications of such problems can be found in [2]. The asymptotic formulas for the eigenvalues and eigenfunctions of boundary problem of Sturm-Liouville type for second order differential equation with retarded argument were obtained in [5]. The asymptotic formulas for the eigenvalues and eigenfunctions of Sturm-Liouville problem with the spectral parameter in the boundary condition were obtained in [6]. In the articles [7,8,9], the asymptotic formulas for the eigenvalues and eigenfunctions of discontinuous Sturm-Liouville problem with transmission conditions and with the boundary conditions which include spectral parameter were obtained. We study the eigenvalues and eigenfunctions of discontinuous boundary-value problem with retarded argument and a spectral parameter in the boundary condition.
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