On the oscillation of forced second order mixed-nonlinear elliptic equations

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 theorems for second order nonlinear forced differential equations

In this paper, a class of second order forced nonlinear differential equation is considered and several new oscillation theorems are obtained. Our results generalize and improve those known ones in the literature.

Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations

Oscillation of Forced Second Order Dynamic Equations on Time Scales

In this paper, by introducing a nonnegative kernel function H(t, s), some oscillation criteria for a forced second-order dynamic equation on time scales are given. AMS Subject Classifications: 34K11, 34C10, 93C70.

An Improvement on the Oscillation of Forced Second Order Nonlinear Differential Equations

In the case of oscillatory potentials, new oscillation criteria are established for the forced nonlinear differential equations ` |x′(t)|αsgnx′(t) ́′ + q(t)|x(t)|sgnx(t) = g(t) (β > α > 0). (*) Our results generalize and improve the main result of Nasr [3] for equation (∗) with α = 1, β > 1 and can be applied to extreme cases such as R∞ t0 q(t)dt = −∞ and R∞ t0 g(t)dt = −∞.