Open Access
Subscription Access
Open Access
Subscription Access
Periodic Indefinite Sturm-Liouville Problems With One Turning Point
Subscribe/Renew Journal
Multiplicity of eigenvalues of the regular indefinite Sturm- Liouville problem ?y"" + qy = ?wy on [a, b] subject to periodic boundary conditions is discussed. A necessary and sufficient condition for the existence of non-simple real eigenvalues is proved. Eigenfunctions corresponding to non-simple real eigenvalues are obtained. In this article, we discuss the interlacing property in one turning point case with periodic boundary conditions.
Keywords
Periodic boundary conditions, Indefinite Sturm Liouville problems, Turning point.
Subscription
Login to verify subscription
User
Font Size
Information
- A. L. Andrew, Correction of finite difference eigenvalues of periodic Sturm-Liouville problems, ANZIAM J., 30(4) (1989), 460–469.
- F. V. Atkinson and D. Jabon, Indefinite Sturm-Liouville problems, in Proc. 1984 Workshop on Spectral Theory of Sturm-Liouville Differential Operators, Argonne National Laboratory, Reprint ANL-84-73, 31–46.
- J. Behrndt, F. Philipp, C. Trunk, Bounds on the non-real spectrum of differential operators with indefinite weights, Mathematische Annalen., 357(1) (2013), 185–213.
- ?I. C¸ elik, G. Gokmen, Approximate solution of periodic Sturm-Liouville problems with Chebyshev collocation method, Appl. Math. Comput., 170(1) (2005), 285–295.
- E. L. Ince, Ordinary Differential Equations, Dover Publications, INC. New York, 1956.
- M. Kikonko, On a non-definite Sturm-Liouville problem in the two turning point caseanalysis and numerical results, J. Appl. Math. Phys., 4 (2016), 1787–1810.
- M. Kikonko, A. B. Mingarelli, Bounds on real and imaginary parts of non-real eigenvalues of a non-definite Sturm-Liouville problem, J. Differential Equations, 261(11), (2016), 6221– 6232.
- A. B. Mingarelli, A survey of the regular weighted Sturm-Liouville problem: the nondefinite case, in Proc. of the Workshop on Applied Differential Equations, Tsinghua University, Beijing, People’s Republic of China, 1985. World Scientific Publ., Singapore and Philadelphia (1986), 109–137.
- A. B. Mingarelli, Indefinite Sturm-Liouville problems, in ‘Ordinary and Partial Differential Equations’, Everitt, W. N. Ed., Lecture Notes in Mathematics 964, Sringer-Verlag, Berlin-New York, (1982), 519–528.
- A. B. Mingarelli, On the existence of non-simple real eigenvalues for general Sturm- Liouville problems, Proc. Amer. Math. Soc., 89, (1983), 457–460.
- A. B. Mingarelli, Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions, Lecture Notes in Mathematics, 989, Springer-Verlag, Berlin, 1983.
- R. G. Richardson, Contributions to the study of oscillation properties of the solutions of linear differential equations of the second order, Amer. J. Math., 40(3) (1918), 283–316.
- B. Xie, J. Qi, Non-real eigenvalues of indefinite Sturm-Liouville problems, J. Differential Equations, 255(8), (2013), 2291–2301.
- U. Y¨ucel, Approximate eigenvalues of periodic Sturm-Liouville problems using differential quadrature method, Appl. Math. Sci. 1(25) (2007), 1217–1229.
- A. Zettl, Sturm-Liouville theory, Mathematical Surveys and Monographs, 121, Amer. Math. Soc., Providence, RI, 2010.
Abstract Views: 127
PDF Views: 0