Bounds for distance between eigenvalues of boundary value problems with retarded argument

References

[1] Akgun, F. A. et al: Discontinuous boundary value problems with retarded argument and eigenparameter-dependent boundary conditions, Mediterr. J. Math. 10 (2013), 277–288.10.1007/s00009-012-0175-7Suche in Google Scholar

[2] Aydemir, K.—Mukhtarov, O. S.: Asymptotic distribution of eigenvalues and eigenfunctions for a multi-point discontinuous Sturm-Liouville problem, Electron. J. Differential Equations 2016 (2016), 1–14.Suche in Google Scholar

[3] Aydemir, K.—Mukhtarov, O. S.: Class of Sturm-Liouville problems with eigenparameter dependent transmission conditions, Numer. Funct. Anal. Optim. 38 (2017), 1260–1275.10.1080/01630563.2017.1316995Suche in Google Scholar

[4] Aydemir, K.—Mukhtarov, O. S.: The eigenvalue problem with interaction conditions at one interior singular point, Filomat 31 (2017), 5411–5420.10.2298/FIL1717411MSuche in Google Scholar

[5] Baker, C. T. H.: Retarded differential equations, J. Comput. Appl. Math. 125 (2000), 309–335.10.1016/B978-0-444-50617-7.50019-7Suche in Google Scholar

[6] Bayramoglu, M. et al: On the spectral properties of the regular Sturm-Liouville Problem with the lag argument for which its boundary conditions depends on the spectral parameter, Turk. J. Math. 26 (2002), 421–431.Suche in Google Scholar

[7] Bayramov, A. et al: Computation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument, Appl. Math. Comp. 191 (2007), 592–600.10.1016/j.amc.2007.02.118Suche in Google Scholar

[8] Bica, A. M. et al: Approximating the solution of second order differential equation with retarded argument, J. Comput. Anal. App., 12 (2010), 37–47.Suche in Google Scholar

[9] Crocco, L.—Chang, S.: Theory of Combustion Instability in Liquid Propellant Rocket Motors, Butterworths, London, 1956.Suche in Google Scholar

[10] Eliason, B.: Distance between zeros of certain differential equations having delayed arguments, Ann. Mat. Pura Appl. 106 (1975), 273–291.10.1007/BF02415034Suche in Google Scholar

[11] Fulton, C. T.: Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 293–308.10.1017/S030821050002521XSuche in Google Scholar

[12] Harkevic A. A.: Auto-oscillations. Gostehizdat, Moscow, 1954.Suche in Google Scholar

[13] Kamenskii, G. A.: On the asymptotic behaviour of solutions of linear differential equations of the second order with retarded argument, Uch. Zap. Mosk. Gos. Univ. 165 (1954), 195–204.Suche in Google Scholar

[14] Kolesovas, J.—Svitra, D.: Mathematical modelling of the combustion process in the chamber of a liquid propellant rocket engine, Lith. Math. J. 15 (1975), 632–642.10.1007/BF00969794Suche in Google Scholar

[15] Levitan, B. M.: Expansion in Characteristic Functions of Differential Equations of the Second Order, GITTL, Moscow, 1950.Suche in Google Scholar

[16] Mukhtarov, O. S. et al: On discontinuous Sturm-Liouville problems with transmission conditions, J. Math. Kyoto Univ. 44 (2004), 779–798.10.1215/kjm/1250281698Suche in Google Scholar

[17] Mukhtarov, O. S.—Aydemir, K.: The eigenvalue problem with interaction conditions at one interior singular point, Filomat 31 (2017), 5411–5420.10.2298/FIL1717411MSuche in Google Scholar

[18] Norkin, S. B.: On boundary problem of Sturm-Liouville type for second-order differential equation with retarded argument, Izv. Vysś. Ućebn. Zaved. Matematika 6 (1958), 203–214.Suche in Google Scholar

[19] Norkin, S. B.: On periodic solutions of a linear homogeneous differential equation of second order with retarded argument, Mat. Sb. 45 (1958), 71–104.Suche in Google Scholar

[20] Norkin, S. B.: Differential Equations of the Second Order with Retarded Argument. Translations of Mathematical Monographs, AMS, Providence, RI, 1972.Suche in Google Scholar

[21] Olgar, H.—Mukhtarov, O. S.: Weak eigenfunctions of two-interval Sturm-Liouville problems together with interaction conditions, J. Math. Phys. 58 (2017), 1–13.10.1063/1.4979615Suche in Google Scholar

[22] Ronto, N. I.: Convergence of the method of trigonometric collocation for nonlinear periodic systems of differential equations with retarded argument, Ukrainian Math. J. 35 (1983), 692–696.10.1007/BF01056239Suche in Google Scholar

[23] Şen, E.—Bayramov, A.: Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the boundary condition, Math. Comput. Modelling 54 (2011), 3090–3097.10.1016/j.mcm.2011.07.039Suche in Google Scholar

[24] Şen, E.—Bayramov, A.: Asymptotic formulations of the eigenvalues and eigenfunctions for a boundary value problem, Math. Meth. Appl. Sci. 36 (2013), 1512–1519.10.1002/mma.2699Suche in Google Scholar

[25] Şen, E. et al: Spectral Problem for the Sturm–Liouville Operator with Retarded Argument Containing a Spectral Parameter in the Boundary Condition, Ukrainian Math. J. 8 (2017), 1263–1277.10.1007/s11253-017-1292-zSuche in Google Scholar

[26] Şen, E.: Sturm-Liouville problems with retarded argument and a finite number of transmission conditions, Electron. J. Differential Equations 2017 (2017), 1–8.Suche in Google Scholar

[27] Şen, E.: Spectral analysis of discontinuous boundary-value problems with retarded argument, J. Math. Phys. Anal. Geo. 14 (2018), 78–99.10.15407/mag14.01.078Suche in Google Scholar

[28] Teodorcik, K. F.: Self-oscillatory Systems, Gostehizdat, Moscow, 1952.Suche in Google Scholar

[29] Titchmarsh, E. C.: Eigenfunctions Expansion Associated With Second Order Differential Equation, Oxford University Press, London, 1962.10.1063/1.3058324Suche in Google Scholar

[30] Yang, C. F.: Trace and inverse problem of a discontinuous Sturm–Liouville operator with retarded argument, J. Math. Anal. Appl. 395 (2012), 30–41.10.1016/j.jmaa.2012.04.078Suche in Google Scholar