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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 280508, 10 pages
Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Received 27 May 2013; Accepted 27 July 2013
Academic Editor: Yansheng Liu
Copyright © 2013 Ruyun Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- F. V. Atkinson, Discrete and Continuous Boundary Problems, Mathematics in Science and Engineering, Vol. 8, Academic Press, New York, NY, USA, 1964.
- A. Jirari, “Second-order Sturm-Liouville difference equations and orthogonal polynomials,” Memoirs of the American Mathematical Society, vol. 113, no. 542, pp. 1–138, 1995.
- W. G. Kelley and A. C. Peterson, Difference Equations: An Introduction with Applications, Academic Press, Boston, Mass, USA, 1991.
- R. P. Agarwal, M. Bohner, and P. J. Y. Wong, “Sturm-Liouville eigenvalue problems on time scales,” Applied Mathematics and Computation, vol. 99, no. 2-3, pp. 153–166, 1999.
- Y. Shi and S. Chen, “Spectral theory of second-order vector difference equations,” Journal of Mathematical Analysis and Applications, vol. 239, no. 2, pp. 195–212, 1999.
- M. Bohner, “Discrete linear Hamiltonian eigenvalue problems,” Computers & Mathematics with Applications, vol. 36, no. 10–12, pp. 179–192, 1998.
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, NY, USA, 1926.
- P. Hess and T. Kato, “On some linear and nonlinear eigenvalue problems with an indefinite weight function,” Communications in Partial Differential Equations, vol. 5, no. 10, pp. 999–1030, 1980.
- A. Anane, O. Chakrone, and M. Moussa, “Spectrum of one dimensional -Laplacian operator with indefinite weight,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2002, no. 17, pp. 1–11, 2002.
- M. Zhang, “Nonuniform nonresonance of semilinear differential equations,” Journal of Differential Equations, vol. 166, no. 1, pp. 33–50, 2000.
- R. Ma, J. Xu, and X. Han, “Global bifurcation of positive solutions of a second-order periodic boundary value problems with indefinite weight,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 5-6, pp. 2119–2125, 2009.
- R. Ma and C. Gao, “Sign-changing solutions of nonlinear boundary value problems of difference equations,” Indian Journal of Pure and Applied Mathematics, vol. 39, no. 4, pp. 323–332, 2008.
- K. J. Brown, “Local and global bifurcation results for a semilinear boundary value problem,” Journal of Differential Equations, vol. 239, no. 2, pp. 296–310, 2007.
- J. Ji and B. Yang, “Eigenvalue comparisons for a class of boundary value problems of second order difference equations,” Linear Algebra and Its Applications, vol. 420, no. 1, pp. 218–227, 2007.
- J. Ji and B. Yang, “Eigenvalue comparisons for second order difference equations with Neumann boundary conditions,” Linear Algebra and Its Applications, vol. 425, no. 1, pp. 171–183, 2007.
- R. Ma and C. Gao, “Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem,” Zeitschrift für Angewandte Mathematik und Physik, vol. 64, no. 3, pp. 493–506, 2013.
- F. R. Gantmaher and M. G. Kreĭn, Oscillation Matrices and Kernels and Small Oscillations of Mechanical Systems, Gosudarstvennym Izdatel'stvom Tehniko-Teoreticheskoj Literatury, Moscow, Russia, 1950.
- R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, Mass, USA, 1990.
- F. R. Gantmacher, The Theory of Matrices. Vol. 1, AMS Chelsea Publishing, New York, NY, USA, 1960.
- V. V. Prasolov, Polynomials, vol. 11 of Algorithms and Computation in Mathematics, Springer, Berlin, Germany, 2010, Translated from the 2001 Russian second edition by Dimitry Leites.