Abstract
Abstract
In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter λ. This nonlinear dependence on λ 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 λ. Problems with Dirichlet boundary conditions as well as with variable endpoints are considered.
Mathematics Subject Classification 2010: 39A21; 39A12.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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