Mathematica Bohemica, Vol. 149, No. 1, pp. 39-47, 2024

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

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

Received June 25, 2022.   Published online January 23, 2023.

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 $\sum_{n=n_0}^\infty p^{-\frc1{\alpha}}(n)<\infty$ (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.
Keywords:  quasi-linear; difference equation; retarded; second-order; oscillation
Classification MSC:  39A10, 39A21

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Affiliations:   George E. Chatzarakis (corresponding author), Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, Marousi 15122, Athens, Greece, e-mail:,; Deepalakshmi Rajasekar, Department of Interdisciplinary Studies, Dr. Ambedkar Law University, Chennai, Tamil Nadu, India, e-mail: Saravanan Sivagandhi, Madras School of Economics, Chennai, Tamil Nadu, India, e-mail:; Ethiraju Thandapani, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, Tamil Nadu, India, e-mail:

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