Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations
نویسندگان
چکیده
We consider the half-linear second-order difference equation Δ rkΦ Δxk ckΦ xk 1 0, Φ x : |x|p−2x, p > 1, where r, c are real-valued sequences. We associate with the above-mentioned equation a linear second-order difference equation and we show that oscillatory properties of the abovementioned one can be investigated using properties of this associated linear equation. Themain tool we use is a linearization technique applied to a certain Riccati-type difference equation corresponding to the above-mentioned one.
منابع مشابه
Half-Linear Dynamic Equations
Abstract. We survey half-linear dynamic equations on time scales. These contain the well-known half-linear differential and half-linear difference equations as special cases, but also other kinds of half-linear equations. Special cases of half-linear equations are the well-studied linear equations of second order. We discuss existence and uniqueness of solutions of corresponding initial value p...
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