Electron. J. Differential Equations, Vol. 2021 (2021), No. 78, pp. 1-15.

Hille-Nehari type non-oscillation criteria for half-linear dynamic equations with mixed derivatives on a time scale

Kazuki Ishibashi

This article deals with half-linear dynamic equations that have two types of derivatives, and obtains sufficient conditions for all solutions to be non-oscillatory. The obtained results extend a previous Hille-Nehari type theorems for problems of dynamic equations. To prove our main result, we use a generalized Riccati inequality. As an application, we apply the main result to self-adjoint Euler type linear differential and difference equations with a changing sign coefficient. The equation selected for this application is of Mathieu type.

Submitted June 16, 2021. Published September 15, 2021.
Math Subject Classifications: 39A21, 34C10.
Key Words: Half-linear dynamic equations; nonoscillation; time scale; Riccati dynamic inequality; linear differential equation; linear difference equation.

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Kazuki Ishibashi
Department of Electronic Control Engineering
National institute of Technology (KOSEN)
Hiroshima College
Toyota-gun 725-023, Japan
email: ishibashi_kazuaoi@yahoo.co.jp

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