Oscillation Theorems for Non-liner Delay Differential Equations

Oscillation theorems for second-order nonlinear delay difference equations

By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation ∆(pn (∆xn) ) + qnf(xn−σ) = 0, n = 0, 1, 2, . . . ,

Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means

By using the general means, we establish some oscillation theorems for the even order delay differential equation (r(t)|x(n−1)(t)|α−1x(n−1)(t))′ + F (t, x[g(t)]) = 0, where α > 0 is a constant, r ∈ C([t0,∞),R+), F ∈ C([t0,∞) × R,R), and g ∈ C([t0,∞),R). The results obtained extend and improve some results known in the literature. 2000 Mathematics Subject Classification: 34K11, 34C10.

Interval Oscillation Theorems for Second Order Nonlinear Partial Delay Differential Equations

Using the integral averaging method and the generalized Riccati technique, we derive new interval oscillation criteria for second order nonlinear partial delay differential equations. These results are different from most known ones in the sense that they are based on information only on a sequence of subintervals of [0,∞) , rather than on the whole [0,∞) . Our results are of a high degree of g...

Oscillation theorems for second order neutral differential equations

In this paper new oscillation criteria for the second order neutral differential equations of the form (E) ` r(t) [x(t) + p(t)x(τ (t))]′ ́ ′ + q(t)x(σ(t)) + v(t)x(η(t)) = 0 are presented. Gained results are based on the new comparison theorems, that enable us to reduce the problem of the oscillation of the second order equation to the oscillation of the first order equation. Obtained comparison ...

Oscillation theorems for systems of linear differential equations