Cheng, Sui Sun; Patula, William T. An existence theorem for a nonlinear difference equation. (English) Zbl 0774.39001 Nonlinear Anal., Theory Methods Appl. 20, No. 3, 193-203 (1993). The authors deal with the following nonlinear difference equation \[ \Delta(\Delta y_{k-1})^{p-1}+s_ k y_ k^{p-1}=0, \qquad k=1,2,3,\dots \tag{1} \] where \(p>1\) and \(\{s_ k\}_ 1^ \infty\) is a real sequence. They establish conditions under which (1) has a positive nondecreasing solution. The main idea is to use the fixed point theorem of Schauder for the equation obtained from (1) by means of a Riccati-type transformation. Reviewer: A.D.Mednykh (Novosibirsk) Cited in 4 ReviewsCited in 63 Documents MSC: 39A10 Additive difference equations Keywords:Riccati transformation; positive solution; nonlinear difference equation PDFBibTeX XMLCite \textit{S. S. Cheng} and \textit{W. T. Patula}, Nonlinear Anal., Theory Methods Appl. 20, No. 3, 193--203 (1993; Zbl 0774.39001) Full Text: DOI References: [2] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities (1988), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0634.26008 [3] Cheng, S. S.; Li, H. J.; Patula, W. T., Bounded and zero convergent solutions of second order difference equations, J. math. Analysis Applic., 141, 463-483 (1989) · Zbl 0698.39002 [4] Griffel, D. H., Applied Functional Analysis, Horwood Series Math. Applic. (1981), Chichester, U.K. · Zbl 0461.46001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.