Mathematica Bohemica, Vol. 148, No. 1, pp. 35-47, 2023
Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations
Govindasamy Ayyappan, George E. Chatzarakis, Thaniarasu Kumar, Ethiraj Thandapani
Received March 22, 2021. Published online March 3, 2022.
Abstract: We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation
D_3y(n)+f(n)y^\beta(\sigma(n))=0,
where $D_3 y(n)=\Delta(b(n)\Delta(a(n)(\Delta y(n))^\alpha))$ is studied. The main idea is to transform the semi-noncanonical operator into canonical form. Then we obtain new oscillation theorems for the studied equation. Examples are provided to illustrate the importance of the main results.
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Affiliations: Govindasamy Ayyappan, Department of Mathematics, Periyar University College of Arts and Science, Pappireddipatti - 636 905, Tamil Nadu, India, e-mail: ayyapmath@gmail.com; George E. Chatzarakis, Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, Marousi 15122, Athens, Greece, e-mail: gea.xatz@aspete.gr, geaxatz@otenet.gr; Thaniarasu Kumar, Department of Mathematics, Periyar University, Salem 636 011, Tamil Nadu, India, e-mail: gtkumarmaths@gmail.com; Ethiraj Thandapani, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, India, e-mail: ethandapani@yahoo.co.in
