Oscillation of second-order quasilinear retarded difference equations via canonical transform

George E. Chatzarakis; Deepalakshmi Rajasekar; Saravanan Sivagandhi; Ethiraju Thandapani

Mathematica Bohemica (2024)

  • Issue: 1, page 39-47
  • ISSN: 0862-7959

Abstract

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We study the oscillatory behavior of the second-order quasi-linear retarded difference equation Δ ( p ( n ) ( Δ y ( n ) ) α ) + η ( n ) y β ( n - k ) = 0 under the condition ∑ n = n 0 ∞ p - 1 α ( n ) < ∞ (i.e., the noncanonical form). Unlike most existing results, the oscillatory behavior of this equation is attained by transforming it into an equation in the canonical form. Examples are provided to show the importance of our main results.

How to cite

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Chatzarakis, George E., et al. "Oscillation of second-order quasilinear retarded difference equations via canonical transform." Mathematica Bohemica (2024): 39-47. <http://eudml.org/doc/299238>.

@article{Chatzarakis2024,
abstract = {We study the oscillatory behavior of the second-order quasi-linear retarded difference equation \[ \Delta (p(n)(\Delta y(n))^\alpha )+\eta (n) y^\beta (n- k)=0 \] under the condition $\sum _\{n=n_0\}^\infty p^\{-\frac\{1\}\{\alpha \}\}(n)<\infty $ (i.e., the noncanonical form). Unlike most existing results, the oscillatory behavior of this equation is attained by transforming it into an equation in the canonical form. Examples are provided to show the importance of our main results.},
author = {Chatzarakis, George E., Rajasekar, Deepalakshmi, Sivagandhi, Saravanan, Thandapani, Ethiraju},
journal = {Mathematica Bohemica},
keywords = {quasi-linear; difference equation; retarded; second-order; oscillation},
language = {eng},
number = {1},
pages = {39-47},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of second-order quasilinear retarded difference equations via canonical transform},
url = {http://eudml.org/doc/299238},
year = {2024},
}

TY - JOUR
AU - Chatzarakis, George E.
AU - Rajasekar, Deepalakshmi
AU - Sivagandhi, Saravanan
AU - Thandapani, Ethiraju
TI - Oscillation of second-order quasilinear retarded difference equations via canonical transform
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 39
EP - 47
AB - We study the oscillatory behavior of the second-order quasi-linear retarded difference equation \[ \Delta (p(n)(\Delta y(n))^\alpha )+\eta (n) y^\beta (n- k)=0 \] under the condition $\sum _{n=n_0}^\infty p^{-\frac{1}{\alpha }}(n)<\infty $ (i.e., the noncanonical form). Unlike most existing results, the oscillatory behavior of this equation is attained by transforming it into an equation in the canonical form. Examples are provided to show the importance of our main results.
LA - eng
KW - quasi-linear; difference equation; retarded; second-order; oscillation
UR - http://eudml.org/doc/299238
ER -

References

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