Geodesic
Asymptotic properties for half-linear difference equations
Mathematica Bohemica, Tome 131 (2006) no. 4, pp. 347-363

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Asymptotic properties of the half-linear difference equation \[ \Delta (a_{n}|\Delta x_{n}|^{\alpha }\mathop {\mathrm sgn}\Delta x_{n} )=b_{n}|x_{n+1}|^{\alpha }\mathop {\mathrm sgn}x_{n+1} \qquad \mathrm{(*)}\] are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to $(*)$ are considered too. Our approach is based on a classification of solutions of $(*)$ and on some summation inequalities for double series, which can be used also in other different contexts.
Asymptotic properties of the half-linear difference equation \[ \Delta (a_{n}|\Delta x_{n}|^{\alpha }\mathop {\mathrm sgn}\Delta x_{n} )=b_{n}|x_{n+1}|^{\alpha }\mathop {\mathrm sgn}x_{n+1} \qquad \mathrm{(*)}\] are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to $(*)$ are considered too. Our approach is based on a classification of solutions of $(*)$ and on some summation inequalities for double series, which can be used also in other different contexts.
DOI : 10.21136/MB.2006.133970
Classification : 39A10, 39A11
Keywords: half-linear second order difference equation; nonoscillatory solutions; Riccati difference equation; summation inequalities 
Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro; Vrkoč, Ivo. Asymptotic properties for half-linear difference equations. Mathematica Bohemica, Tome 131 (2006) no. 4, pp. 347-363. doi: 10.21136/MB.2006.133970
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