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)...
Saved in:
| Date: | 1994 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1994
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5731 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511954351685632 |
|---|---|
| author | Vitrychenko, I. E. Вітриченко, І. Є. |
| author_facet | Vitrychenko, I. E. Вітриченко, І. Є. |
| author_sort | Vitrychenko, I. E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:16:47Z |
| description | 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. |
| first_indexed | 2026-03-24T03:21:06Z |
| format | Article |
| fulltext |
0031
0032
0033
0034
0035
0036
0037
0038
0039
0040
|
| id | umjimathkievua-article-5731 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:21:06Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b0/d5f4cf6e2da0abdce58a017c1cf11cb0.pdf |
| spelling | umjimathkievua-article-57312020-03-19T09:16:47Z On oscillation of solutions of a nonautonomous quasilinear second-order equation Про коливання розв'язків одного квазілінійного рівняння другого порядку Vitrychenko, I. E. Вітриченко, І. Є. 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. Одержано достатні умови для початкових значень коливних за умови $t = ω$ нетривіальних розв'язків неавтономного квазілінійного рівняння вигляду $y'' \pm \lambda (t)y = F(t,y,y'),$, $t ∈ Δ = [a, ω[,-∞ < a < ω ≤ + ∞, λ(t) > 0, λ(t) ∈ C_Δ^{(1)},$ $|F((t,x,y))| ≤ L(t)(|x|+|y|)^{1+α}, L(t) ≥ -0, α ∈ [0,+∞[,$ $ F: Δ × R^2 →R, F ∈ C_{Δ × R^2}, R$ — відповідно множина дійсних чисел і двовимірний евклідів дійсний простір. Institute of Mathematics, NAS of Ukraine 1994-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5731 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 4 (1994); 347–356 Український математичний журнал; Том 46 № 4 (1994); 347–356 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5731/8147 https://umj.imath.kiev.ua/index.php/umj/article/view/5731/8148 Copyright (c) 1994 Vitrychenko I. E. |
| spellingShingle | Vitrychenko, I. E. Вітриченко, І. Є. On oscillation of solutions of a nonautonomous quasilinear second-order equation |
| title | On oscillation of solutions of a nonautonomous quasilinear second-order equation |
| title_alt | Про коливання розв'язків одного квазілінійного рівняння другого порядку |
| title_full | On oscillation of solutions of a nonautonomous quasilinear second-order equation |
| title_fullStr | On oscillation of solutions of a nonautonomous quasilinear second-order equation |
| title_full_unstemmed | On oscillation of solutions of a nonautonomous quasilinear second-order equation |
| title_short | On oscillation of solutions of a nonautonomous quasilinear second-order equation |
| title_sort | on oscillation of solutions of a nonautonomous quasilinear second-order equation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5731 |
| work_keys_str_mv | AT vitrychenkoie onoscillationofsolutionsofanonautonomousquasilinearsecondorderequation AT vítričenkoíê onoscillationofsolutionsofanonautonomousquasilinearsecondorderequation AT vitrychenkoie prokolivannârozv039âzkívodnogokvazílíníjnogorívnânnâdrugogoporâdku AT vítričenkoíê prokolivannârozv039âzkívodnogokvazílíníjnogorívnânnâdrugogoporâdku |