Asymptotic properties for half-linear difference equations

Mariella Cecchi; Zuzana Došlá; Mauro Marini; Ivo Vrkoč

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 4, page 347-363
  • ISSN: 0862-7959

Abstract

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Asymptotic properties of the half-linear difference equation Δ ( a n | Δ x n | α s g n Δ x n ) = b n | x n + 1 | α s g n x n + 1 ( * ) 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.

How to cite

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Cecchi, Mariella, et al. "Asymptotic properties for half-linear difference equations." Mathematica Bohemica 131.4 (2006): 347-363. <http://eudml.org/doc/249895>.

@article{Cecchi2006,
abstract = {Asymptotic properties of the half-linear difference equation \[ \Delta (a\_\{n\}|\Delta x\_\{n\}|^\{\alpha \}\mathop \{\mathrm \{s\}gn\}\Delta x\_\{n\} )=b\_\{n\}|x\_\{n+1\}|^\{\alpha \}\mathop \{\mathrm \{s\}gn\}x\_\{n+1\} \qquad \mathrm \{(*)\}\] 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.},
author = {Cecchi, Mariella, Došlá, Zuzana, Marini, Mauro, Vrkoč, Ivo},
journal = {Mathematica Bohemica},
keywords = {half-linear second order difference equation; nonoscillatory solutions; Riccati difference equation; summation inequalities; half-linear second order difference equation; nonoscillatory solutions; Riccati difference equation},
language = {eng},
number = {4},
pages = {347-363},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic properties for half-linear difference equations},
url = {http://eudml.org/doc/249895},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Cecchi, Mariella
AU - Došlá, Zuzana
AU - Marini, Mauro
AU - Vrkoč, Ivo
TI - Asymptotic properties for half-linear difference equations
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 4
SP - 347
EP - 363
AB - Asymptotic properties of the half-linear difference equation \[ \Delta (a_{n}|\Delta x_{n}|^{\alpha }\mathop {\mathrm {s}gn}\Delta x_{n} )=b_{n}|x_{n+1}|^{\alpha }\mathop {\mathrm {s}gn}x_{n+1} \qquad \mathrm {(*)}\] 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.
LA - eng
KW - half-linear second order difference equation; nonoscillatory solutions; Riccati difference equation; summation inequalities; half-linear second order difference equation; nonoscillatory solutions; Riccati difference equation
UR - http://eudml.org/doc/249895
ER -

References

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  8. Half-Linear Differential Equations, Handbook of Differential Equations, Ordinary Differential Equations I., A. Cañada, P. Drábek, A. Fonda (eds.), Elsevier, Amsterdam, 2004. (2004) Zbl1090.34027MR2166491
  9. Nonoscillation criteria for half-linear second order difference equations, Comput. Math. Appl. 42 (2001), 453–464. (2001) MR1838006
  10. 10.1080/10236100309487534, J. Differ. Equ. Appl. 9 (2003), 49–61. (2003) MR1958302DOI10.1080/10236100309487534
  11. 10.1016/0022-247X(83)90088-4, J. Math. Anal. Appl. 91 (1983), 9–29. (1983) MR0688528DOI10.1016/0022-247X(83)90088-4
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