Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro Positive solutions for singular discrete boundary value problems. (English) Zbl 1070.39006 Abstr. Appl. Anal. 2004, No. 4, 271-283 (2004). The paper deals with the second-order difference equation (1) \(\Delta(a_n\Phi_p (\Delta x_n)) = g(n, x_{n+1})\), where \(\Delta x_n = x_{n+1} - x_n,\) \(\{ a_n \}\) is a positive real sequence, \(g\) is a positive continuous function on \(\mathbb{N} \times(0,u_0)\), \(0<u_0\leq\infty\), and \(\Phi_p(u)=| u|^{p-2}u\) with \(p>1\). The function \(g\) can be unbounded with respect to the second variable in a right neighborhood of zero. The authors give conditions for the existence of decaying solutions of (1), i.e. positive solutions \(\{ x_n \}\) with \(\Delta x_n < 0\) and \(\lim_n x_n=0\). Reviewer: Victor I. Tkachenko (Kyïv) Cited in 1 Document MSC: 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis 34B16 Singular nonlinear boundary value problems for ordinary differential equations Keywords:second-order difference equation; decaying solution PDFBibTeX XMLCite \textit{M. Cecchi} et al., Abstr. Appl. Anal. 2004, No. 4, 271--283 (2004; Zbl 1070.39006) Full Text: DOI EuDML