Oscillatory properties of second-order hybrid functional differential equation via Leighton transform
Kumar S. VIDHYAA, Ganesh PURUSHOTHAMAN, John R. GRAEF, Ethiraju THANDAPANI
Received October 1, 2025. Published online May 27, 2026.
Abstract: The authors discuss the oscillation of the second order hybrid trinomial differential equation with a deviating argument
(a(t) y^{\prime}(t))^{\prime}+p_1(t) y(t)-p_2(t) y^{\alpha}(\sigma(t))=0 by making use of a Leighton oscillation preserving transformation. Under certain conditions, they give new criteria to exclude certain types of nonoscillatory solutions. As a by-product, they establish oscillation criteria for the mixed type equation (a_1(t) y^{\prime}(t))^{\prime}+p_1(t) y(t)-p_2(t) y^{\alpha}(\sigma(t))-p_3(t) y^{\gamma}(\tau(t))=0, where $\sigma$ is a delay and $\tau$ is an advanced argument. Examples are provided to illustrate the novelty and importance of the main results.
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Affiliations: Kumar S. Vidhyaa, Department of Mathematics, Easwari Engineering College, 162, Bharathi Salai, Ramapuram, Chennai, Tamil Nadu 600089, India, e-mail: vidhyacertain@gmail.com; Ganesh Purushothaman, Department of Mathematics, St. Joseph's College of Engineering, Chennai, Tamil Nadu 600119, India, e-mail: gpmanphd@gmail.com; John R. Graef (corresponding author), Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Ave, Chattanooga, TN37403, USA, e-mail: johngraef9@gmail.com; Ethiraju Thandapani, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, Tamil Nadu 600005, India, e-mail: ethandapani@yahoo.co.in
