Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations

oleh: Fišnarová Simona, Došlý Ondřej

Format: Article
Diterbitkan: SpringerOpen 2008-01-01

Deskripsi

<p/> <p>We consider the half-linear second-order difference equation <inline-formula> <graphic file="1687-1847-2008-438130-i1.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1847-2008-438130-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1847-2008-438130-i3.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-1847-2008-438130-i4.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1847-2008-438130-i5.gif"/></inline-formula> 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 above-mentioned one can be investigated using properties of this associated linear equation. The main tool we use is a linearization technique applied to a certain Riccati-type difference equation corresponding to the above-mentioned one.</p>