[1] Ahn H J. On random transverse vibrations of rotating beam with tip mass. Quart J Mech Appl Math, 1983, 39:97-109 [2] Aliyev Z S. Basis properties in Lp of systems of root functions of a spectral problem with spectral parameter in a boundary condition. Differential Equations, 2011, 47:766-777 [3] Aliyev Z S. On basis properties of root functions of a boundary value problem containing a spectral parameter in the boundary conditions. Dokl Math, 2013, 87:137-139 [4] Aliyev Z S, Dunyamalieva A A. Defect basis property of a system of root functions of a Sturm-Liouville problem with spectral parameter in the boundary conditions. Differ Equ, 2015, 51:1249-1266 [5] Aliyev Z S, Dunyamalieva A A. Basis properties of root functions of the Sturm-Liouville problem with a spectral parameter in the boundary conditions. (Russian) Dokl Akad Nauk, 2013, 451:487-491; translation in Dokl Math, 2013, 88:441-445 [6] Aliyev Z S, Guliyeva S B. Properties of natural frequencies and harmonic bending vibrations of a rod at one end of which is concentrated inertial load. J Differential Equations, 2017, 263:5830-5845 [7] Atkinson F. Discrete and Continuous Boundary Problems. New York:Academic Press, 1964 [8] Belinskiy B, Dauer J P, Xu Y. Inverse scattering of accustic waves in an oceas with ice cover. Appl Anal, 1996, 61:255-283 [9] Binding P. A hierarchy of Sturm-Liouville problems. Math Meth Appl Sci, 2003, 26:349-357 [10] Bhattacharyya T, Binding P, Seddighi K. Two-parameter right definite Sturm-Liouville problems with eigenparameter-dependent boundary conditions. Proc Edinburgh Math Soc, 2001, 131:45-58 [11] Binding P, Browne Patrick J. Application of two parameter eigencurves to Sturm-Liouville problems with eigenparameter-dependent boundary condition. Proc Edinburgh Math Soc, 1995, 125:1205-1218 [12] Binding P, Browne Patrick J, Seddighi K. Sturm-Liouville problems with eigenparameter dependent boundary conditions. Proc Edinburgh Math Soc, 1993, 37:57-72 [13] Bohner M, DoŠlý O, Kratz W. An oscillation theorem for discrete eigenvalue problems. Rocky Mountain J Math, 2003, 33:1233-1260 [14] Currie S, Love D. Hierarchies of difference boundary value problems II-Application. Quaest Math, 2014, 37:371-392 [15] Curgus B, Dijksma A, Read T. The linearization of boundary eigenvalue problems and reproducing kernel Hilbert spaces. Linear Algebra Appl, 2001, 329:97-136 [16] Dijksma A, Langer H, H S V de Snoo. Symmetric Sturm-Liouville operators with eigenvalue dependending boundary conditions. CMS Conf Proc, 1987, 8:87-116 [17] Dijksma A, Langer H, H S V de Snoo. Eigenvalues and pole functions of Hamiltonian systems with eigenvalue depending boundary condition. Math Nachr, 1993, 161:107-154 [18] Dijksma A, Langer H. Operator theory and ordinary differential operators, Lectures on operator theory and its applications. Fields Inst Monogr, 1996, 3:73-139 [19] Došlý O, Kratz W. Oscilation theorems for symplectic difference systems. J Difference Equ Appl, 2007, 13:585-605 [20] Fulton C. Two-point boundary value problems with eigenvalue parameter contained in the boundary condition. Proc Edniburgh Math Soc, 1977, 77:293-308 [21] Fulton C, Pruess S. Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions. J Math Anal Appl, 1979, 71:431-462 [22] Gao C H. On the linear and nonlinear discrete second-order Neumann boundary value problems. Appl Math Comput, 2014, 233:62-71 [23] Gao C H, Li X L, Ma R Y. Eigenvalues of a linear fourth-order differential operator with squared spectral parameter in a boundary condition. Mediterr J Math, 2018, 15:107 [24] Gao C H, Ma R Y. Eigenvalues of discrete Sturm-Liouville problems with eigenparameter dependent boundary conditions. Linear Algebra Appl, 2016, 503:100-119 [25] Gao C H, Li X L, Zhang F. Eigenvalues of discrete Sturm-Liouville problems with nonlinear eigenparameter dependent boundary conditions. Quaest Math, 2018, 41:773-797 [26] Gao C H, Ma R Y, Zhang F. Spectrum of discrete left definite Sturm-Liouville problems with eigenparameter-dependent boundary conditions. Linear Multilinear Algebra, 2017, 65:1905-1923 [27] Gao C H, Ma R Y. Eigenvalues of discrete linear second-order periodic and antiperiodic eigenvalue problems with sign-changing weight. Linear Algebra Appl, 2015, 467:40-56 [28] Hartman P. Difference equations:Disconjugacy, principal solutions, Green's functions, complety monotonicity. Trans Amer Math Soc, 1978, 246:1-30 [29] Harmsen B J, Li A. Discrete Sturm-Liouville problems with nonlinear parameter in the boundary conditions. J Difference Equ Appl, 2007, 13:639-653 [30] Harmsen B J, Li A. Discrete Sturm-Liouville problems with parameter in the boundary conditions. J Difference Equ. Appl, 2002, 8:969-981 [31] Jirari A. Second-order Sturm-Liouville difference equations and orthogonal polynomials. Mem Amer Math Soc, 2004, 294:104-112 [32] Kapustin N Yu. On the uniform convergence of the Fourier series for a spectral problem with squared spectral parameter in the boundary condition. Differ Equ, 2010, 46:1507-1510 [33] KapustinN Yu. On the uniform convergence in the class C1 of the Fourier series for a spectral problem with squared spectral parameter in the boundary condition. Differ Equ, 2011, 47:1408-1413 [34] Kapustin N Yu. On the basis property of the system of eigenfunctions of a problem with squared spectral parameter in a boundary condition. Differ Equ, 2015, 51:1274-1279 [35] Kelley W G, Peterson A C. Difference Equations:An Introduction with Applications (2nd ed). CA:Academic Press, 2001 [36] Kerimov N B, Poladov R G. Basis properties of the system of eigenfunctions in the Sturm-Liouville problem with a spectral parameter in the boundary conditions. Dokl Math, 2012, 85:8-13 [37] Koprubasi T, Yokus N. Quadratic eigenparameter dependent discrete Sturm-Liouville equations with spectral singularities. Appl Math Comput, 2014, 244:57-62 [38] Koprubasi Turhan, Mohapatra R N. Spectral properties of generalized eigenparameter dependent discrete Sturm-Liouville type equation. Quaest Math, 2017, 40:491-505 [39] Kratz W. Discrete Oscillation. J Difference Equ Appl, 2003, 9:135-147 [40] Langer R E. A problem in diffusion or in the flow of heat for a solid in contact with fluid. Tohoku Math J, 1932, 35:360-375 [41] Ma R Y, Gao C H, Lu Y Q. Spectrum theory of second-order difference equations with indefinite weight. J Spectr Theory, 2018, 8:971-985 [42] Poisson M. Sur la manière d'éxperimer les fonctions par des series de quantités, et sur l'usage de cette transformation dans la résolution de différents problèms. Paris:Ecole Polytechnique de Paris, 1820, 18emé cahier, Vol. XI [43] Shi Y M, Chen S Z. Spectral theory of second-order vector difference equations. J Math Anal Appl, 1999, 239:195-212 [44] Sun H Q, Shi Y. Eigenvalues of second-order difference equations with coupled boundary conditions. Linear Algebra Appl, 2006, 414:361-372 [45] Wang Y, Shi Y M. Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions. J Math Anal Appl, 2005, 309:56-69 [46] Gao C H. Solutions to discrete multiparameter periodic boundary value problems involving the p-Laplacian via critical point theory. Acta Mathematica Scientia, 2014, 34B(4):1225-1236 [47] Luo H. Spectral theory of linear weighted Sturm-Liouville eigenvalue problems. Acta Mathematica Scientia, 2017, 37B(3):427-449 [48] Gao C H, Lv L, Wang Y L. Spectra of a discrete Sturm-Liouville problem with eigenparameterdependent boundary conditions in Pontryagin space. Quaestiones Mathematicae, 2019. DOI:10.2989/16073606.2019.1680456 |