Eigenvalue comparisons for a class of boundary value problems of second order difference equations
This paper deals with the structure of eigenvalues of the boundary value problem for the second order difference equation \[ \Delta(r_{i-1}\Delta y_{i-1})-b_i y_i+\lambda a_iy_i=0, 1\leq i\leq n, y_0-\tau y_1=y_{n+1}-\delta y_n=0 \] under the assumption that the \(a_i\)'s can be negative at some \(i\), \(1\leq i\leq n\). Especially, the authors focus on the comparison of all eigenvalues as the coefficients \(\{a_i\}_{i=1}^{n}\), \(\{b_i\}_{i=1}^{n}\), \(\{r_i\}_{i=1}^{n}\) and the parameter \(\tau, \delta\) change. The results extend the authors earlier results to a more general setting, allowing some \(a_i\)'s to be negative [\textit{J. Ji, B. Yang}, J. Math. Anal. Appl. 320, No. 2, 964--972 (2006; Zbl 1111.39012)].
scientific article; zbMATH DE number 5126064
scientific article