Boundary Value Problem with Retarded Argument and a Finite Number of Transmission Conditions
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In the present paper, our boundary value problem is Sturm–Liouville problem with retarded argument and transmission conditions at the finitely many points of discontinuity. This is the first work containing several points of discontinuity in the theory of differential equations with retarded argument. The main purpose of this paper is to obtain asymptotic formulas for the eigenvalues and corresponding eigenfunctions of this boundary value problem. The simplicity of the eigenvalues is proved. In special case when our problem with retarded argument and transmission conditions at one point of discontinuity, the obtained results coincide with the corresponding results in Bayramov et al. (Appl Math Comput 191, 592–600, 2007).
KeywordsSturm–Liouville problem Retarded argument Transmission conditions Discontinuous boundary value problems Asymptotic of eigenvalues
Mathematics Subject Classification34L16 94A20 65L15.
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