An existence theorem for a nonlinear difference equation. (English) Zbl 0774.39001

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.


39A10 Additive difference equations
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