Oscillation of Three-Dimensional Time Scale Systems with Fixed Point Theorems

Abstract

Oscillation and nonoscillation theories play very important roles in gaining information about the long-time behavior of solutions of a system. For example, for nonlinear control systems, we need to find a Lyapunov function to determine if a system is stable, and in some cases it is very hard to find an appropriate Lyapunov function. Therefore, we investigate the asymptotic behavior of nonoscillatory solutions as well as the existence of such solutions so that one can determine the limit behavior.