Li, Wan-Tong; Cheng, Sui Sun Characterizing conditions for the existence of nonoscillatory solutions of a discrete Emden-Fowler equation with summable coefficients. (English) Zbl 0971.39003 Dyn. Syst. Appl. 9, No. 3, 457-461 (2000). The author presents necessary and sufficient conditions for the existence of nonoscillatory solutions for the discrete Emden-Fowler differential equation \[ \Delta ^2x_{n-1}+a_n|x_n|^\gamma \text{ sign} x_n=0,\quad n=0,1,2,... \] in the case when \(\{ a_n\}\) is a sequence of real numbers satisfying the conditions \[ -\infty <\lim_{n\rightarrow \infty}\sum_{s=0}^{n-1}a_s<\infty, \] and \(A_n\equiv \sum_{s=n}^\infty a_s\geq 0\) for all \(n=0,1,2,...\). It is analysed the sublinear case \(0<\gamma <1\) as well as the superlinear case \(\gamma >1\). Reviewer: Nicolae Cotfas (Bucureşti) Cited in 5 Documents MSC: 39A10 Additive difference equations 39A12 Discrete version of topics in analysis 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) Keywords:nonlinear difference equations; nonoscillatory solution; discrete Emden-Fowler equation PDFBibTeX XMLCite \textit{W.-T. Li} and \textit{S. S. Cheng}, Dyn. Syst. Appl. 9, No. 3, 457--461 (2000; Zbl 0971.39003)