Comparison theorems for half-linear second order difference equations. (English) Zbl 1090.39500

Mařík, Robert

Arch. Math., Brno 36, Suppl., 513-518 (2000).

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 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.

Reviewer: Pavel Řehák (Brno)

MSC:

39A10

Additive difference equations

Keywords:

half-linear difference equation; comparison theorem

Citations:

Zbl 0982.39004