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

AbstractIn 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)Φα(x′(t)))′+p0(t)Φα(x(t))+∑i=1npi(t)Φβi(x(t))=e(t),t≠τk,x(τk+)=akx(τk),x′(τk+)=bkx′(τk), where t⩾t0, k∈N; Φ⁎(u)=|u|⁎−1u; {τk} is the impulse moments sequence with 0⩽t0=τ0<τ1<τ2<⋯<τk<⋯ and limk→∞τk=∞; α=p/q, p, q are odds, and the exponents satisfyβ1>⋯>βm>α>βm+1>⋯>βn>0. Some known results are generalized and improved. Examples are also given to illustrate the effectiveness and non-emptiness of our results