On unbounded solutions of the first order ordinary differential equations
The article is concerned with Cauchy problem Gx(x, ξ) + H (x, G(x, ξ)) = 0, G(ξ, ξ)= + ∞ Let H(x, y), Hy(x,y) ∈ C(R2) and H(x, y) ≻ a1 |y|1+a +a2 where a1, a2 ≻ 0. Then there exists the unique solution G(x, ξ) of Cauchy problem and it is general solution of this equation.
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2001-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/34432 |
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| _version_ | 1823857876883472384 |
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| author | Gintautas Gudynas |
| author_facet | Gintautas Gudynas |
| author_sort | Gintautas Gudynas |
| collection | DOAJ |
| description |
The article is concerned with Cauchy problem
Gx(x, ξ) + H (x, G(x, ξ)) = 0,
G(ξ, ξ)= + ∞
Let H(x, y), Hy(x,y) ∈ C(R2) and
H(x, y) ≻ a1 |y|1+a +a2
where a1, a2 ≻ 0. Then there exists the unique solution G(x, ξ) of Cauchy problem and it is general solution of this equation.
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| format | Article |
| id | doaj-art-f8dccf5c04734f98a4484e7dfff4615a |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2001-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-f8dccf5c04734f98a4484e7dfff4615a2025-02-11T18:14:36ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2001-12-0141spec.10.15388/LMR.2001.34432On unbounded solutions of the first order ordinary differential equationsGintautas Gudynas0Klaipedos University The article is concerned with Cauchy problem Gx(x, ξ) + H (x, G(x, ξ)) = 0, G(ξ, ξ)= + ∞ Let H(x, y), Hy(x,y) ∈ C(R2) and H(x, y) ≻ a1 |y|1+a +a2 where a1, a2 ≻ 0. Then there exists the unique solution G(x, ξ) of Cauchy problem and it is general solution of this equation. https://www.zurnalai.vu.lt/LMR/article/view/34432 |
| spellingShingle | Gintautas Gudynas On unbounded solutions of the first order ordinary differential equations Lietuvos Matematikos Rinkinys |
| title | On unbounded solutions of the first order ordinary differential equations |
| title_full | On unbounded solutions of the first order ordinary differential equations |
| title_fullStr | On unbounded solutions of the first order ordinary differential equations |
| title_full_unstemmed | On unbounded solutions of the first order ordinary differential equations |
| title_short | On unbounded solutions of the first order ordinary differential equations |
| title_sort | on unbounded solutions of the first order ordinary differential equations |
| url | https://www.zurnalai.vu.lt/LMR/article/view/34432 |
| work_keys_str_mv | AT gintautasgudynas onunboundedsolutionsofthefirstorderordinarydifferentialequations |