Araştırma Makalesi
The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations-2
Öz
We consider the singular initial value problem for the second order differential equation. We interested in the existence of positive solutions and proved an easily applicable theorem on the existence of positive solutions to initial-value problems for second-order nonlinear singular differential equations. The previously established result on the existence of positive solution by Agarwal and O'Regan is not easy for the applications due to very complex definition of a new function and their properties in the statement of their theorem. We used the Lebesgue dominated convergence theorem and the Schauder--Tychonoff theorem in the proof of the main result. The main result can be easily applied for the singular and regular type of problems.
Anahtar Kelimeler
Emden-Fowler equation Second order equations Existence Lane-Emden equation Fixed points
Kaynakça
- [1] R. P. Agarwal, D. O’Regan, Second order initial value problems of Lane-Emden type, Appl. Math. Lett., 20 (2007), 1198-1205.
- [2] A. Aslanov, A new theorem on the existence of positive solutions of singular initial-value problem for second order differential equations, Commun. Adv. Math. Sci., 2(1) (2019), 22-26.
- [3] A. Constantin, On the existence of positive solutions of second-order differential equations, Ann. Mat. Pura Appl., 184(2005), 131-138.
- [4] T. Ertem, A. Zafer, Asymptotic integration of second-order nonlinear differential equations via principal and nonprincipal solutions, Appl. Math. Comput., 219 (2013), 5876–5886.
- [5] T. Ertem, A. Zafer, Existence of solutions for a class of nonlinear boundary value problems on half-line, Bound. Value Probl., 2012(2012), Article Number 43.
- [6] T. Ertem, A. Zafer, Monotone positive solutions for a class of second-order nonlinear differential equations, . J. Comput. Appl. Math., 259(2014), 672-681.
- [7] Z. Yin, Monotone positive solutions of second-order nonlinear differential equations, Nonlinear Anal., 54 (2003), 391-403.
- [8] Z. Zhao, Positive Solutions of Nonlinear Second Order Ordinary Differential Equations, Proc. Amer. Math. Soc., 121 (1994), 465-469.
Yıl 2020,
, 203 - 207, 22.12.2020
Öz
Kaynakça
- [1] R. P. Agarwal, D. O’Regan, Second order initial value problems of Lane-Emden type, Appl. Math. Lett., 20 (2007), 1198-1205.
- [2] A. Aslanov, A new theorem on the existence of positive solutions of singular initial-value problem for second order differential equations, Commun. Adv. Math. Sci., 2(1) (2019), 22-26.
- [3] A. Constantin, On the existence of positive solutions of second-order differential equations, Ann. Mat. Pura Appl., 184(2005), 131-138.
- [4] T. Ertem, A. Zafer, Asymptotic integration of second-order nonlinear differential equations via principal and nonprincipal solutions, Appl. Math. Comput., 219 (2013), 5876–5886.
- [5] T. Ertem, A. Zafer, Existence of solutions for a class of nonlinear boundary value problems on half-line, Bound. Value Probl., 2012(2012), Article Number 43.
- [6] T. Ertem, A. Zafer, Monotone positive solutions for a class of second-order nonlinear differential equations, . J. Comput. Appl. Math., 259(2014), 672-681.
- [7] Z. Yin, Monotone positive solutions of second-order nonlinear differential equations, Nonlinear Anal., 54 (2003), 391-403.
- [8] Z. Zhao, Positive Solutions of Nonlinear Second Order Ordinary Differential Equations, Proc. Amer. Math. Soc., 121 (1994), 465-469.
Toplam 8 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 22 Aralık 2020 |
| Gönderilme Tarihi | 27 Temmuz 2020 |
| Kabul Tarihi | 14 Aralık 2020 |
| Yayımlandığı Sayı | Yıl 2020 |
Kaynak Göster
The published articles in CAMS are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License..