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 $y'' \pm \lambda (t)y = F(t,y,y'),$, where $t ∈ Δ = [a, ω[,-∞ < a < ω ≤ + ∞, λ(t) > 0, λ(t) ∈ C_Δ^{(1)...
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| Datum: | 1994 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1994
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5731 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | Sufficient conditions are obtained for the initial values of nontrivial oscillating (for $t = ω$) solutions of the nonautonomous quasilinear equation
$y'' \pm \lambda (t)y = F(t,y,y'),$,
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. |
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