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discrete spectrum; property BD; discrete variational principle; discrete Wirtinger’s inequality; singular difference operators; oscillation; difference operator
We investigate oscillation and spectral properties (sufficient conditions for discreteness and boundedness below of the spectrum) of difference operators B(y)_{n+k} = {{(-1)}^n\over w_k} \Delta^n (p_k \Delta^n y_k).
[1] Bohner M.: Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions. J. Math. Anal. Appl. 199 (1996), 804-826. DOI 10.1006/jmaa.1996.0177 | MR 1386607
[2] Bohner M., Došlý O.: Disconjugacy and transformations for symplectic systems. Rocky Mountain J. Math. 27 (1997), 707-743. DOI 10.1216/rmjm/1181071889 | MR 1490271
[3] Došlý O.: Reciprocity principle for Sturm-Liouville difference equations and some of its applications. Proceedings of SICDEA. Veszprem, 1995, pp. 145-153. MR 1636320
[4] Hinton D. B., Lewis R. T.: Spectral analysis of second order difference equations. J. Math. Anal. Appl. 63 (1978), 421-438. DOI 10.1016/0022-247X(78)90088-4 | MR 0611455 | Zbl 0392.39001
[5] Hinton D. B., Lewis R. T.: Discrete spectra criteria for singular differential operators with middle terms. Math. Proc. Cambridge Philos. Soc. 77 (1975), 337-347. MR 0367358 | Zbl 0298.34018
[6] Hartman P.: Difference equations: disconjugacy, principal solutions, Green's function, complete monoticity. Trans. Amer. Math. Soc. 246 (1978), 1-30. MR 0515528
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