Conjugacy criteria for second order linear difference equations

Ondrej Dosly, Pavel Rehak

Address. Ondrej Dosly, Mathematical Institute, Academy of Sciences, Zizkova 22, 616 62 Brno, CZECH REPUBLIC

Pavel Rehak, Masaryk University, Faculty of Sciences, Department of Mathematics, Janackovo nam. 2a, 662 95 Brno, CZECH REPUBLIC


Abstract. We establish conditions which guarantee that the second order difference equation $$\Delta ^2x_k+p_k x_{k+1}=0$$ possesses a nontrivial solution with at least two generalized zero points in a given discrete interval

AMSclassification. 39A10

Keywords. Discrete conjugacy criteria, discrete Riccati equation, phase function, generalized zero points