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Conjugacy criteria for second order linear difference equations

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Ondrej Dosly, Pavel Rehak
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** 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

** E-mail:**

**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