Spectral and oscillation theory for general second order Sturm-Liouville difference equations
نویسندگان
چکیده
منابع مشابه
Spectral and oscillation theory for general second order Sturm-Liouville difference equations
In this article we establish an oscillation theorem for second order Sturm-Liouville difference equations with general nonlinear dependence on the spectral parameter l. This nonlinear dependence on l 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 re...
متن کاملOverview of Weyl–Titchmarsh Theory for Second Order Sturm–Liouville Equations on Time Scales
In this paper we present an overview of the basic Weyl–Titchmarsh theory for second order Sturm–Liouville equations on time scales. We construct the m(λ)function, the Weyl solution, and the Weyl disk. We justify the terminology “disk” by its geometric properties, show explicitly the coordinates of the center of the disk, and calculate its radius. We show that the dichotomy regarding the squarei...
متن کاملRelative Oscillation Theory for Sturm–liouville Operators Extended
We extend relative oscillation theory to the case of Sturm–Liouville operators Hu = r−1(−(pu′)′ + qu) with different p’s. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein’s spectral shift function inside essential spectral gaps.
متن کاملSturm-Liouville Oscillation Theory for Differential Equations and Applications to Functional Analysis
We study the connection between second-order differential equations and their corresponding difference equations. With this connection in mind, we investigate quantitative and qualitative properties of the zeros of the solutions of differential/difference equations and of the eigenvalues of the associated Jacobi matrices. In particular, we study various applications of the Sturm-Liouville Oscil...
متن کاملOscillation criteria for second-order linear difference equations
A non-trivial solution of (1) is called oscillatory if for every N > 0 there exists an n > N such that X,X n + , 6 0. If one non-trivial solution of (1) is oscillatory then, by virtue of Sturm’s separation theorem for difference equations (see, e.g., [S]), all non-trivial solutions are oscillatory, so, in studying the question of whether a solution {x,> of (1) is oscillatory, it is no restricti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2012
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2012-82