Hille-Nehari type non-oscillation criteria for half-linear dynamic equations with mixed derivatives on a time scale
Texas State University, Department of Mathematics
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.
Half-linear dynamic equations, Nonoscillation, Time scale, Riccati dynamic inequality, Linear differential equation, Linear difference equation
Ishibashi, K. (2021). Hille-Nehari type non-oscillation criteria for half-linear dynamic equations with mixed derivatives on a time scale. <i>Electronic Journal of Differential Equations, 2021</i>(78), pp. 1-15.