Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

Bailey, P.B., Everitt, W.N., Weidmann, J., Zettl, A.: Regular approximations of singular Sturm–Liouville problems. Results Math. 23, 3–22 (1993) Bailey, P.B., Everitt, W.N., Zettl, A.: The SLEIGN2 Sturm–Liouville code, ACM TOMS. ACM Trans. Math. Softw. 21, 1–15 (2001) Binding, P.A., Browne, P.J., Seddighi, K.: Sturm–Liouville problems with eigenparameter dependent boundary conditions. Proc. Edinb. Math. Soc. 37(2), 57–72 (1993) Binding, P.A., Browne, P.J., Watson, B.A.: Equivalence of inverse Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. J. Math. Anal. Appl. 291, 246–261 (2004) Brown, M., Greenberg, L., Marletta, M.: Convergence of regular approximations to the spectra of singular fourth order Sturm–Liouville problems. Proc. R. Soc. Edinb., Sect. A 128(5), 907–944 (1998) Cai, J., Zheng, Z.: Matrix representations of Sturm–Liouville problems with coupled eigenparameter-dependent boundary conditions and transmission conditions. Math. Methods Appl. Sci. 41, 3495–3508 (2018) El-Gebeily, M.A.: Regular approximation of singular self-adjoint differential operators. IMA J. Appl. Math. 68, 471–489 (2003) Fulton, C.T.: Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. R. Soc. Edinb. A 77, 293–308 (1977) Fulton, C.T.: Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions. Proc. R. Soc. Edinb. A 87, 1–34 (1980) Kato, T.: Pertubation Theory for Linear Operators, 2nd edn. Springer, Heidelberg (1980) Mukhtarov, O.S., Aydemir, K.: Eigenfunction expansion for Sturm–Liouville problems with transmission conditions at one interior point. Acta Math. Sci. Ser. B Engl. Ed. 35(3), 639–649 (2015) Nursultanov, M., Rozenblum, G.: Eigenvalue asymptotics for the Sturm–Liouville operator with potential having a strong local negative singularity. Opusc. Math. 37(1), 109–139 (2017) Papageorgiou, N., Radulescu, V., Repovs, D.: Nonlinear Analysis—Theory and Methods. Springer Monographs in Mathematics. Springer, Cham (2019) Radulescu, V.: Finitely many solutions for a class of boundary value problems with superlinear convex nonlinearity. Arch. Math. (Basel) 84(6), 538–550 (2005) Reed, M., Simon, B.: Methods of Modern Mathematical Physics I: Functional Analysis. Academic Press, San Diego (1972) Teschl, G.: On the approximation of isolated eigenvalues of ordinary differential operators. Proc. Am. Math. Soc. 136(7), 2473–2476 (2008) Walter, J.: Regular eigenvalue problems with eigenvalue parameter in the boundary condition. Math. Z. 133, 301–312 (1973) Weidmann, J.: Linear Operators in Hilbert Space. Springer, New York (1980) Weidmann, J.: Spectral Theory of Ordinary Differential Operators. Lectures Notes in Math., vol. 1258. Springer, Berlin (1987) Yang, C., Bondarenko, N., Xu, X.: An inverse problem for the Sturm–Liouville pencil with arbitrary entire functions in the boundary condition. Inverse Probl. Imaging 14(1), 153–169 (2020) Zettl, A.: Sturm–Liouville Theory. Mathematical Surveys Monographs, vol. 121. Am. Math. Soc., Providence (2005) Zhang, M.: Regular approximation of singular Sturm–Liouville problems with transmission conditions. Appl. Math. Comput. 247, 511–520 (2014) Zhang, M., Li, K., Wang, Y.: Regular approximation of linear Hamiltonian operators with two singular endpoints. J. Math. Anal. Appl. (2020). https://doi.org/10.1016/j.jmaa.2019.123758 Zhang, M., Sun, J., Zettl, A.: The spectrum of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and its approximation. Results Math. 63, 1311–1330 (2013) Zhang, M., Sun, J., Zettl, A.: Eigenvalues of limit-point Sturm–Liouville problems. J. Math. Anal. Appl. 419, 627–642 (2014) Zheng, Z., Cai, J., Li, K., Zhang, M.: A discontinuous Sturm–Liouville problem with boundary conditions rationally dependent on the eigenparameter. Bound. Value Probl. 2018, 103 (2018). https://doi.org/10.1186/s13661-018-1023-x