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Zbl 1090.39500
Mař\'ik, Robert
Comparison theorems for half-linear second order difference equations. (English)
[J] Arch. Math., Brno 36, Suppl., 513-518 (2000). ISSN 0044-8753; ISSN 1212-5059/e

In the paper the half-linear difference equation $$\Delta \Bigl (R_k\Phi (\Delta z_k)\Bigr )+C_k\Phi (z_{k+1})=0 $$ with $p$-laplacian is studied. There are formulated new type of comparison theorems for this equation using the variational technique, which was stated in {\it P. Řehák} [Czech. Math. J. 51, 303--321 (2001; Zbl 0982.39004)]. The main difference between the presented results and the cited results lies in the another types of boundary conditions for the argument of discrete $p$-degree functional. This enables to obtain information about solution of the mentioned equation given by another initial condition than that in the cited paper.
[Pavel Řehák (Brno)]

MSC 2000:: *39A10 Difference equations

Keywords: half-linear difference equation; comparison theorem

Citations: Zbl 0982.39004

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