Mathematica Bohemica, Vol. 146, No. 3, pp. 263-278, 2021
Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments
Srinivasan Selvarangam, Sethurajan A. Rupadevi, Ethiraju Thandapani, Sandra Pinelas
Received July 10, 2019. Published online September 30, 2020.
Abstract: In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation $\Delta^3(x_n+a_n x_{n-l} +b_n x_{n+m})+p_n x_{n-k} - q_n x_{n+r}=0,\quad n\geq n_0$ via Banach contraction principle. Examples are provided to illustrate the main results. The results obtained in this paper extend and complement some of the existing results.
Keywords: third order; nonoscillation; delay and advanced arguments; neutral difference equation
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Affiliations: Srinivasan Selvarangam, Sethurajan Ammaiappan Rupadevi, Department of Mathematics, Presidency College (Autonomous), 100 Kamarajar Salai, Chepauk, Chennai 600005, India, e-mail: selvarangam.9962@gmail.com, rupalect@gmail.com; Ethiraju Thandapani, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Wallajah Road, Navalar Nagar, Chepauk, Triplicane, Chennai 600005, India, e-mail: ethandapani@yahoo.co.in; Sandra Pinelas, Departamento de Ciências Exatas e Engenharia, Academia Militar, Av. Conde Castro Guimarães, 2720-113 Amadora, Portugal, e-mail: sandra.pinelas@gmail.com
