Oscillation of second order differential equations with mixed nonlinearities

Forced oscillation of second-order differential equations with mixed nonlinearities

where t ≥ t > , n ≥  is a natural number, βi ≥  (i = , , . . . ,n) are constants, r ∈ C([t,∞),R), qj, τj, e ∈ C([t,∞),R), r(t) > , r′(t)≥ , qj(t)≥  (j = , , , . . . ,n), e(t)≤ . We also assume that there exists a function τ ∈ C([t,∞),R) such that τ (t) ≤ τj(t) (j = , , , . . . ,n), τ (t)≤ t, limt→∞ τ (t) =∞, and τ ′(t) > . We consider only those solutions x of equation (....

Oscillation of Second-Order Neutral Functional Differential Equations with Mixed Nonlinearities

and Applied Analysis 3 and established some sufficient conditions for oscillation of 1.6 under the conditions 1.3 and

Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities

New Oscillation Criteria for Second-Order Delay Differential Equations with Mixed Nonlinearities

Yuzhen Bai and Lihua Liu School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China Correspondence should be addressed to Yuzhen Bai, [email protected] Received 10 January 2010; Accepted 17 June 2010 Academic Editor: Binggen Zhang Copyright q 2010 Y. Bai and L. Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestrict...

Interval Criteria for Oscillation of Second-order Impulsive Differential Equation with Mixed Nonlinearities

We establish sufficient conditions for the oscillation of all solutions to the second-order impulsive differential equation ` r(t)x′(t) ́′ + p(t)x′(t) + q(t)x(t) + n X i=1 qi(t)|x(t)|i sgnx(t) = e(t), t 6= τk, x(τk ) = akx(τk), x (τk ) = bkx (τk). The results obtained in this paper extend some of the existing results and are illustrated by examples.