Abstract
Sufficient conditions are obtained for the initial values of nontrivial oscillating (for t=ω) solutions of the nonautonomous quasilinear equation
wheret ∈ Δ=[a, ω[,-∞ <a < ω ≤+ ∞, λ(t) > 0, λ(t) ∈ C (1)Δ , |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.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 347–356, April, 1994.
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Vitrychenko, I.E. On oscillation of solutions of a nonautonomous quasilinear second-order equation. Ukr Math J 46, 362–372 (1994). https://doi.org/10.1007/BF01060406
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DOI: https://doi.org/10.1007/BF01060406