Oscillatory property of solutions of second order differential equations

Nonrectifiable Oscillatory Solutions of Second Order Linear Differential Equations

The second order linear differential equation (p(x)y′)′ + q(x)y = 0 , x ∈ (0, x0] is considered, where p, q ∈ C1(0, x0], p(x) > 0, q(x) > 0 for x ∈ (0, x0]. Sufficient conditions are established for every nontrivial solutions to be nonrectifiable oscillatory near x = 0 without the Hartman–Wintner condition.

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Oscillatory Behavior of Second Order Neutral Differential Equations

Oscillation criteria are obtained for solutions of forced and unforced second order neutral differential equations with positive and negative coefficients. These criteria generalize those of Manojlović, Shoukaku, Tanigawa and Yoshida (2006).

Existence of oscillatory solutions of forced second order delay differential equations

Oscillatory and Asymptotic Behavior of Solutions of Second Order Neutral Delay Differential Equations with “maxima”

The authors establish some new criteria for the oscillation and asymptotic behavior of all solutions of the equation. (a(t)(x(t) + p(t)x(τ(t)))) + q(t) max [σ(t),t] x(s) = 0, t ≥ t0 ≥ 0, where a(t) > 0, q(t) ≥ 0, τ(t) ≤ t, σ(t) ≤ t, α is the ratio of odd positive integers, and ∫∞ 0 dt a(t) < ∞. Examples are included to illustrate the results. AMS Subject Classification: 34K11, 34K99