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

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

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 (....

On Oscillation of Second-Order Nonlinear Neutral Functional Differential Equations

In this paper, some sufficient conditions are established for the oscillation of second-order neutral functional differential equation [ r(t)[x(t)+ p(t)x(τ(t))]′ ]′+q(t) f (x(σ(t))) = 0, t ≥ t0, where ∫ ∞ t0 dt/r(t) = ∞, or ∫ ∞ t0 dt/r(t) < ∞, 0 ≤ p(t) ≤ p0 < ∞. The results obtained here complement and improve some known results in the literature. 2010 Mathematics Subject Classification: 39A21,...

Oscillation of Second-Order Neutral Dynamic Equations with Mixed Arguments

We present some new oscillation criteria for a class of half-linear second-order neutral dynamic equations with mixed arguments. An example is given to illustrate the main results.

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