The following equation is considered in this paper:
where
α,
β and
γ are real parameters and
γ>0. This equation is referred to as Mathieu's equation when
γ=2. The parameters determine whether all solutions of this equation are oscillatory or nonoscillatory. Our results provide
parametric conditions for oscillation and nonoscillation; there is a feature in which it is very easy to check whether these conditions are satisfied or not. Parametric oscillation and nonoscillation regions are drawn to help understand the obtained results.