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Computation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument. (English) Zbl 1193.34173
Summary: A discontinuous boundary value problem with retarded argument and with transmission conditions at the point of discontinuity are investigated. In the special case that our problem is continuous (i.e. when $\delta =1$ in below) the obtained results coincidewith corresponding results in [{\it S. B. Norkin}, Izv. Vyssh. Uchebn. Zaved., Mat. 1958, No. 6(7), 203--214 (1958; Zbl 0122.09904)].

##### MSC:
 34L16 Numerical approximation of eigenvalues and of other parts of the spectrum 34A36 Discontinuous equations 34A37 Differential equations with impulses
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##### References:
 [1] Kamenskii, G. A.: On the asymptotic behaviour of solutions of linear differential equations of the second order with retarded argument. Moskov. GoS univ. Uć. zap. 165, No. Mat. 7, 195-2004 (1954) [2] Norkin, S. B.: On boundary problem of Sturm -- Liouville type for second-order differential equation with retarded argument. Izv. vysś. Ućebn. zaved. Matematika 6, No. 7, 203-214 (1958) [3] Nersesjan, A. B.: Expansion in eigenfunctions of some non-selfadjoint boundary problems. Sibirsk. mat Ź. 2, 428-453 (1961) [4] Jablonski, M.; Twardowska, K.: On boundary value problems for differential equations with retarded argument. Univ. iagellonce acta math. Iss. 26, 29-36 (1987) [5] Demidenko, G. V.; Likhoshvai, V. A.: On differential equations with retarded argument. Sib. mat. Zh. 46, No. 3, 417-430 (2005) · Zbl 1224.34204 [6] Demidenko, G. V.; Matveeva, I. I.: Asymptotic properties of solution of delay differential equations. Vestnik MGU. Ser.: matematika, mekhanika, informatika 5, No. 3, 20-28 (2005) · Zbl 1249.34211 [7] Norkin, S. B.: Differential equations of the second order with retarded argument. Translations of mathematical monographs 31 (1972) · Zbl 0234.34080 [8] Bellman, R.; Cook, K. L.: Differential-difference equations. (1963) · Zbl 0105.06402