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Comparison theorems for half-linear second order difference equations

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*Robert Marik*

**Address.** Dept. of Mathematics, Mendel University of Agriculture
and Forestry Brno, Zemedelska 1, 613 00 Brno,

Czech Republic
**E-mail:** marik@mendelu.cz

**Abstract.** In the paper new comparison theorems for half--linear
difference equation $$ \Delta\Bigl(R_k\Phi(\Delta z_k)\Bigr)+C_k\Phi(z_{k+1})=0
$$ are derived. The main tool is variational technique developed for half--linear
difference equations in \v Reh\' ak \cite{marik.R}.

**AMSclassification.** 39A10

**Keywords.** Half-linear difference equation, comparison theorem