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)Phi(alpha)(x'(t)))' + p(0)(t)Phi(alpha)(x(t)) + Sigma(n)(i=1) pi(t)Phi(beta i)(x(t)) = e(t), t not equal tau k, x(tau(+)(k)) = a(k)x(tau(k)), x'(tau(+)(k)) = b(k)x'(tau k), where t >= t(0), k epsilon N: Phi(*)(u) = vertical bar u vertical bar(*-1) u: {tau(k)} is the impulse moments sequence with 0 <= tau(0) = tau(0) < tau(1) < tau(2) < ... < tau(k) < ... and lim(k ->infinity) tau(k) = infinity; alpha = p/q, p, q are odds, and the exponents satisfy beta(1) > ... > beta(m) > alpha > beta(m+1) > ... > beta(n) > 0, Some known results are generalized and improved. Examples are also given to illustrate the effectiveness and non-emptiness of our results. (C) 2011 Elsevier Inc. All rights reserved.