New Interval Oscillation Criteria for Forced Second-Order Differential Equations with Nonlinear Damping

We introduce and prove some new interval oscillation criteria for a general class of forced second-order differential equations (E) : ( r(t)k1(x, x′) )′ + p(t)k2(x, x′)x′ + q(t)f(x) = e(t), t ≥ t0, where the functions k1(u, v), k2(u, v) and f(u) satisfy some general conditions. Our interval oscillation criteria and their proofs are different than previously published ones, and it is based on (i): a construction of a global supersolution of the generalized Riccati differential equation (R): ω′ = A1(t)|ω(t)| +A2(t)|ω(t)| +B(t), t ≥ T , by using the classic Riccati transformation of a nonoscillatory solution of the main equation (E), on (ii): a construction of a pair of local subsolutions of equation (R) under a new oscillatory condition on the coefficients of the main equation (E) and on (iii): a pointwise comparison principle between all suband supersolutions of equation (R). Mathematics Subject Classification: 34C10