Interval oscillation criteria for second-order forced impulsive differential equations with mixed nonlinearities

In this paper, by arithmetic–geometric mean inequality and Riccati transformation, interval oscillation criteria are established for second-order forced impulsive differential equation with mixed nonlinearities of the form { ( r ( t ) Φ α ( x ′ ( t ) ) ) ′ + p 0 ( t ) Φ α ( x ( t ) ) + ∑ i = 1 n p i ( t ) Φ β i ( x ( t ) ) = e ( t ) , t ≠ τ k , x ( τ k + ) = a k x ( τ k ) , x ′ ( τ k + ) = b k x ′ ( τ k ) , where t ⩾ t 0 , k ∈ N ; Φ ⁎ ( u ) = | u | ⁎ − 1 u ; { τ k } is the impulse moments sequence with 0 ⩽ t 0 = τ 0 < τ 1 < τ 2 < ⋯ < τ k < ⋯ and lim k → ∞ τ k = ∞ ; α = p / q , p, q are odds, and the exponents satisfy β 1 > ⋯ > β m > α > β m + 1 > ⋯ > β n > 0 . Some known results are generalized and improved. Examples are also given to illustrate the effectiveness and non-emptiness of our results.