Conjugacy criteria for second order linear difference equations
Archivum mathematicum, Tome 34 (1998) no. 2, pp. 301-310 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We establish conditions which guarantee that the second order difference equation \[\Delta ^2x_k+p_k x_{k+1}=0\] possesses a nontrivial solution with at least two generalized zero points in a given discrete interval
We establish conditions which guarantee that the second order difference equation \[\Delta ^2x_k+p_k x_{k+1}=0\] possesses a nontrivial solution with at least two generalized zero points in a given discrete interval
Classification : 39A10, 39A12
Keywords: Discrete conjugacy criteria; discrete Riccati equation; phase function; generalized zero points
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Došlý, Ondřej; Řehák, Pavel. Conjugacy criteria for second order linear difference equations. Archivum mathematicum, Tome 34 (1998) no. 2, pp. 301-310. http://geodesic.mathdoc.fr/item/ARM_1998_34_2_a7/

[1] Ahlbrandt, C. D., Clark, S. L., Hooker, J. W., Patula, W. T.: A Discrete interpretation of Reid’s Roundabout Theorem for generalized differential systems. to appear in Comp. Math. Appl. | MR

[2] Ahlbrandt, C. D.,Peterson, A.: Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati equations. Kluwer, Dordrecht/Boston/London 1996. | MR | Zbl

[3] Agarwal, R. P.: Difference Equations and Inequalities, Theory, Methods and Applications, Pure and Appl. Math., M. Dekker, New York-Basel-Hong Kong, 1992. | MR | Zbl

[4] Bohner, M.: Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions. J. Math. Anal. Appl 199 (1996), 804-826. | MR | Zbl

[5] Bohner, M., Došlý, O.: Disconjugacy and transformation for symplectic systems. to appear in Rocky Mountain J. Math. | MR

[6] Došlý, O.: The existence of conjugate points for self-adjoint differential equations. Proc. Roy. Soc. Edinburgh 113A (1989), 73-85. | MR

[7] Došlý, O.: Conjugacy criteria for second order differential equations. Rocky Mountain J. Math 23 (1993), 849-861. | MR

[8] Došlý, O.: Oscillation theory of differential and difference equations. Proc. Conf. Ordinary Diff. Equations and Appl., Poprad 1996.

[9] Došlý, O.: Linear Hamiltonian systems – continuous versus discrete. Proc. 7$^{th}$ Colloquium on Diff. Equations, Plovdiv 1996.

[10] Kelley, W. G., Peterson, A.: Difference Equations: An Introduction with Applications, Acad. Press, San Diego, 1991. | MR

[11] Minargelli, A. B.: Volterra-Stieltjes Integral Equations and Ordinary Differential Expressions. LN No. 989, Springer Verlag, New York 1983.

[12] Müller-Pfeiffer, E.: Existence of conjugate points for second and fourth order differential equations. Proc. Roy. Soc. Edinburgh 89A (1981), 281-291. | MR

[13] Müller-Pfeiffer, E.: Nodal domains of one– or two–dimensional elliptic differential equations. Z. Anal. Anwendungen 7 (1988), 135-139. | MR

[14] Reid, W. T.: Generalized linear differential systems. J. Math. Mech. 8 (1959), 705-726. | MR | Zbl

[15] Swanson, C. A.: Comparison and Oscillation Theory of Linear Differential Equations, Acad. Press, New York, 1968. | MR | Zbl

[16] Sturm, J. C. F.: Mémoire sur le équations differentielles linéaries du second ordre. Journal de Mathématiques Pures et Appliquées 1 (1836), 106-186.

[17] Tipler, F. J.: General relativity and conjugate differential equations. J. Differential Equations 30 (1978), 165-174. | MR

[18] Willet, D.: Classification of second order linear differential equations with respect to oscillation. Advances in Mathematics 3 (1969), 594-623. | MR