On a special critical case of stability of a nonautonomous essentially nonlinear system

We obtain sufficient conditions for the Lyapunov stability of the trivial solution of a nonautonomous essentially nonlinear differential system in a special critical case. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1711–1718, December, 2005.     

Critical Cases of the π-Stability of a Nonautonomous Quasilinear Equation of the nth Order

We establish sufficient conditions for the n-stability of the trivial solution of a quasilinear equation of the nth order.     

Global λ-Stability of One Nonautonomous Quasilinear Second-Order Equation

We establish sufficient conditions for the -stability of the trivial solution of one quasilinear differential equation of the second order.     

Critical Cases of the π-Stability of a Nonautonomous Essentially Nonlinear Equation of the nth order

We establish sufficient conditions for the -stability of the trivial solution of an essentially nonlinear equation of the nth order.     

On oscillation of solutions of a nonautonomous quasilinear second-order equation

Sufficient conditions are obtained for the initial values of nontrivial oscillating (for t=ω) solutions of the nonautonomous quasilinear equation $$y'' \pm \lambda (t)y = F(t,y,y'),$$ wheret ∈ Δ=[a, ω[,-∞ <a < ω ≤+ ∞, λ(t) > 0, λ(t) ∈ C _Δ ⁽¹⁾ , |F((t,x,y))|≤L(t)(|x|+|y|)^1+α, L(t) ≥-0, α ∈ [0,+∞[, F: Δ × R² →R,F ∈C _Δ×R ²,R is the set of real numbers, and R² is the two-dimensional real Euclidean space.