Oscillation of Third-Order Thomas–Fermi-Type Nonlinear Differential Equations with an Advanced Argument

Ganesh Purushothaman, Ekambaram Chandrasekaran, John R. Graef () and Ethiraju Thandapani
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Ganesh Purushothaman: Department of Mathematics, St. Joseph’s College of Engineering, Chennai 600119, India
Ekambaram Chandrasekaran: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai 600062, India
John R. Graef: Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
Ethiraju Thandapani: Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India

Mathematics, 2024, vol. 12, issue 24, 1-13

Abstract: In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of Thomas–Fermi-type third-order nonlinear differential equations with advanced argument of the form ( a 2 ( t ) ( a 1 ( t ) y ′ ( t ) ) ′ ) ′ − q ( t ) y α ( σ ( t ) ) = 0 , under the assumptions that ∫ t 0 ∞ 1 a 2 ( t ) d t < ∞ and ∫ t 0 ∞ 1 a 1 ( t ) d t = ∞ . The results are achieved by transforming the equation into a canonical-type equation and then applying integral averaging techniques and the comparison method to obtain oscillation criteria for the transformed equation. This in turn will imply the oscillation of the original equation. Several examples are provided to illustrate the significance of the main results.

Keywords: third-order; Thomas–Fermi equation; oscillation; advanced argument (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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