New Hille Type and Ohriska Type Criteria for Nonlinear Third-Order Dynamic Equations

Taher S. Hassan, Qingkai Kong, Rami Ahmad El-Nabulsi () and Waranont Anukool
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Taher S. Hassan: Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Qingkai Kong: Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA
Rami Ahmad El-Nabulsi: Center of Excellence in Quantum Technology, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailand
Waranont Anukool: Center of Excellence in Quantum Technology, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2022, vol. 10, issue 21, 1-12

Abstract: The objective of this paper is to derive new Hille type and Ohriska type criteria for third-order nonlinear dynamic functional equations in the form of a 2 ( ζ ) φ α 2 a 1 ζ φ α 1 x Δ ( ζ ) Δ Δ + q ( ζ ) φ α x ( g ( ζ ) ) = 0 , on a time scale T , where Δ is the forward operator on T , α 1 , α 2 , α > 0 , and g , q , a i , i = 1 , 2 , are positive r d -continuous functions on T , and φ θ ( u ) : = u θ − 1 u . Our results in this paper are new and substantial for dynamic equations of the third order on arbitrary time scales. An example is included to illustrate the results.

Keywords: Hille type; Ohriska type; third order; time scales; dynamic equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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