Comparison theorems for half-linear second order difference equations

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