Spectral and oscillation theory for general second order Sturm-Liouville difference equations

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Authors	ŠIMON HILSCHER Roman
Year of publication	2012
Type	Article in Periodical
Magazine / Source	Advances in Difference Equations
MU Faculty or unit	Faculty of Science
Citation
Doi	http://dx.doi.org/10.1186/1687-1847-2012-82
Field	General mathematics
Keywords	Sturm-Liouville difference equation; Discrete symplectic system; Oscillation theorem; Finite eigenvalue; Finite eigenfunction; Generalized zero; Quadratic functional
Attached files	ade_dslosc_online_version.pdf
Description	In this paper we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter lambda. This nonlinear dependence on lambda is allowed both in the leading coefficient and in the potential. We extend the traditional notions of eigenvalues and eigenfunctions to this more general setting. Our main result generalizes the recently obtained oscillation theorem for second order Sturm-Liouville difference equations, in which the leading coefficient is constant in lambda. Problems with Dirichlet boundary conditions as well as with variable endpoints are considered.
Related projects:	Diferenční rovnice a dynamické rovnice na time scales III