Oscillation criteria for second-order half-linear advanced differential equations arising in bacterial population dynamics
Ganesh PURUSHOTHAMAN, Ekambaram CHANDRASEKARAN, George E. CHATZARAKIS, Ethiraju THANDAPANI
Received May 13, 2025. Published online May 27, 2026.
Abstract: This study presents novel oscillation criteria for second-order half-linear differential equations with advanced mixed nonlinearities, which commonly arise in modeling bacterial population growth with competing species. By applying the arithmetic-geometric mean inequality, we reduce the original equation to a half-linear differential equation in advanced form. Using comparison methods and successive substitution techniques, we establish new oscillation conditions that explicitly incorporate advanced arguments. In addition, we provide illustrative examples that highlight the improvements and effectiveness of our results compared with existing criteria in the literature.
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Affiliations: Ganesh Purushothaman, Department of Mathematics, St. Joseph's College of Engineering, Jeppiaar Nagar, Old Mamallapuram Road, Chennai-600 119, India, e-mail: gpmanphd@gmail.com; Ekambaram Chandrasekaran, Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, 34, Gandhi Mandapam Road, Chennai-600 085, Tamil Nadu, India, e-mail: drchandrasekarane@veltech.edu.in; George E. Chatzarakis (corresponding author), 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; Ethiraju Thandapani, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Navalar Nagar, Chepauk, Triplicane, Chennai-600005, Tamil Nadu, India, e-mail: ethandapani@yahoo.co.in