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Zbl 0774.39001
Cheng, Sui Sun; Patula, William T.
An existence theorem for a nonlinear difference equation.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 20, No.3, 193-203 (1993). ISSN 0362-546X

The authors deal with the following nonlinear difference equation $$\Delta(\Delta y\sb{k-1})\sp{p-1}+s\sb k y\sb k\sp{p-1}=0, \qquad k=1,2,3,\dots \tag 1$$ where $p>1$ and $\{s\sb k\}\sb 1\sp \infty$ 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.
[A.D.Mednykh (Novosibirsk)]
MSC 2000:
*39A10 Difference equations

Keywords: Riccati transformation; positive solution; nonlinear difference equation

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