2020 Volume 10 Issue 5
Article Contents

Ekin Uğurlu. ON THE EIGENVALUES OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1897-1911. doi: 10.11948/20190281
Citation: Ekin Uğurlu. ON THE EIGENVALUES OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 1897-1911. doi: 10.11948/20190281

ON THE EIGENVALUES OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS

  • In this paper we investigate the properties of eigenvalues of some boundary-value problems generated by second-order Sturm-Liouville equation with distributional potentials and suitable boundary conditions. Moreover, we share a necessary condition for the problem to have an infinitely many eigenvalues. Finally, we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of the data.
    MSC: 34B09, 65H17
  • 加载中
  • [1] F. V. Atkinson, Discrete and continuous boundary problems, Academic Press, 1964.

    Google Scholar

    [2] C. Bennewitz and W. N. Everitt, On second-order left-definite boundary value problems, in Ordinary differential equations and operators, Springer, 1983, 31-67.

    Google Scholar

    [3] E. A. Coddington and N. Levinson, Theory of ordinary differential equations, Tata McGraw-Hill Education, 1955.

    Google Scholar

    [4] J. Dieudonné, Foundations of modern analysis, Read Books Ltd, 2011.

    Google Scholar

    [5] J. Eckhardt, F. Gesztesy, R. Nichols and G. Teschl, Weyl-titchmarsh theory for sturm-liouville operators with distributional potentials, arXiv preprint arXiv: 1208.4677, 2012.

    Google Scholar

    [6] S. Ge, W. Wang and J. Suo, Dependence of eigenvalues of a class of fourth-order sturm-liouville problems on the boundary, Applied Mathematics and Computation, 2013, 220, 268-276. doi: 10.1016/j.amc.2013.06.029

    CrossRef Google Scholar

    [7] E. Hille, Lectures on ordinary differential equations, 1969.

    Google Scholar

    [8] K. Jorgens, Spectral Theory of Second-order Ordinary Differential Operators: Lectures Delivered at Aarhus Universitet 1962/63, Aarhus Universitet, Matematisk Institut, 1964.

    Google Scholar

    [9] Q. Kong, H. Wu and A. Zettl, Dependence of the nth sturm-liouville eigenvalue on the problem, Journal of differential equations, 1999, 156(2), 328-354. doi: 10.1006/jdeq.1998.3613

    CrossRef Google Scholar

    [10] Q. Kong and A. Zettl, Dependence of eigenvalues of sturm-liouville problems on the boundary, journal of differential equations, 1996, 126(2), 389-407. doi: 10.1006/jdeq.1996.0056

    CrossRef Google Scholar

    [11] K. Li, J. Sun and X. Hao, Dependence of eigenvalues of 2 n th order boundary value transmission problems, Boundary Value Problems, 2017, 2017(1), 1-14.

    Google Scholar

    [12] K. Li, J. Sun and X. Hao, Eigenvalues of regular fourth-order sturm-liouville problems with transmission conditions, Mathematical Methods in the Applied Sciences, 2017, 40(10), 3538-3551. doi: 10.1002/mma.4243

    CrossRef Google Scholar

    [13] A. M. Savchuk and A. A. Shkalikov, Sturm-liouville operators with singular potentials, Mathematical Notes, 1999, 66(6), 741-753. doi: 10.1007/BF02674332

    CrossRef Google Scholar

    [14] E. Uğurlu, Regular third-order boundary value problems, Applied Mathematics and Computation, 2019, 343, 247-257. doi: 10.1016/j.amc.2018.09.046

    CrossRef Google Scholar

    [15] E. Uğurlu, Regular fifth-order boundary value problems, Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43, 2105-2121. doi: 10.1007/s40840-019-00794-w

    CrossRef Google Scholar

    [16] E. Uğurlu and E. Bairamov, The spectral analysis of a nuclear resolvent operator associated with a second order dissipative differential operator, Computational Methods and Function Theory, 2017, 17(2), 237-253. doi: 10.1007/s40315-016-0185-8

    CrossRef Google Scholar

    [17] Q. Yang, W. Wang and X. Gao, Dependence of eigenvalues of a class of higher-order sturm-liouville problems on the boundary, Mathematical Problems in Engineering, 2015, 2015.

    Google Scholar

    [18] A. Zettl, Sturm-liouville theory, mathematical surveys and monographs, American Mathematical Society, Providence, 2005, 121.

    Google Scholar

    [19] M. Zhang and Y. Wang, Dependence of eigenvalues of sturm-liouville problems with interface conditions, Applied Mathematics and Computation, 2015, 265, 31-39. doi: 10.1016/j.amc.2015.05.002

    CrossRef Google Scholar

Article Metrics

Article views(2541) PDF downloads(425) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint