Non-oscillation criterion for generalized Mathieu-type differential equations with bounded coefficients

The following equation is considered in this work: x + ( − α + β cos ⁡ ( ρ t ) + f ( t ) ) x = 0 , {equation*} x + (-α + β cos (ρ t) + f(t))x = 0, {equation*} where the parameters α α and β β are real numbers, the frequency ρ ρ is a positive real number, and f : [ 0 , ∞ ) → R f\!: [0,∞ ) → R is a continuous bounded function, i.e., there exists a positive constant f ∗ f^* such that | f ( t ) | ≤ f ∗ |f(t)| ≤ f^* for t ≥ 0 t≥ 0 . This equation is generally referred to as the Mathieu equation when f ∗ = 0 f^*=0 . This work proposes a non-oscillation theorem that can be applied even if <m