Publication details
Spectral and oscillation theory for general second order Sturm-Liouville difference equations
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Advances in Difference Equations |
| MU Faculty or unit | |
| 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 | |
| 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. |
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