On oscillation of solutions of a nonautonomous quasilinear second-order equation - Vitrychenko, I. E. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
Sufficient conditions are obtained for the initial values of nontrivial oscillating (for $t = ω$) solutions of the nonautonomous quasilinear equation$y'' ± λ (t)y = F(t,y,y'),$,where $t ∈ 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 × R^2 →R, F ∈ C_{Δ × R^2}, R$ is the set of real numbers, and $R^2$ is the two-dimensional real Euclidean space.