Kamenev Type Oscillation Criteria for Nonlinear Difference Equations

Kamenev-type Oscillation Criteria for Second-order Quasilinear Differential Equations

We obtain Kamenev-type oscillation criteria for the second-order quasilinear differential equation (r(t)|y′(t)|α−1y′(t))′ + p(t)|y(t)|β−1y(t) = 0 . The criteria obtained extend the integral averaging technique and include earlier results due to Kamenev, Philos and Wong.

Kamenev-type oscillation criteria for second order nonlinear dynamic equations on time scales

Oscillation Criteria for First-order Forced Nonlinear Difference Equations

where (i) {p(n)}, {e(n)} are sequences of real numbers; (ii) {qi(n)}, i= 1,2, are sequences of positive real numbers; (iii) λ, μ are ratios of positive odd integers with 0 < μ < 1 and λ > 1. By a solution of equation (1, i), i= 1,2,3, we mean a nontrivial sequence {x(n)}which is defined for n ≥ n0 ∈ N = {0,1,2, . . .} and satisfies equation (1, i), i = 1,2,3, and n = 1,2, . . . . A solution {x(...

Oscillation Criteria for Certain Third Order Nonlinear Difference Equations

Some new criteria for the oscillation of all solutions of third order nonlinear difference equations of the form ∆ a(n)(∆ 2 x(n)) α + q(n)f (x[g(n)]) = 0 and ∆ a(n)(∆ 2 x(n)) α = q(n)f (x[g(n)]) + p(n)h(x[σ(n)]) with ∞ a −1/α (n) < ∞ are established.

Kamenev-type Oscillation Criteria for Second-Order Linear Delay Dynamic Equations