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

Advances in Difference Equations

Roman imon Hilscher¹ 

[1] Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

关键词: Sturm-Liouville difference equation;    discrete symplectic system;    oscillation theorem;    finite eigenvalue;    finite eigenfunction;    generalized zero;    quadratic functional;   

DOI  :  10.1186/1687-1847-2012-82

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY