| Title:
|
A new look at an old comparison theorem (English) |
| Author:
|
Jaroš, Jaroslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
151-156 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval $[a,b)$ when it is known that certain majorant Riccati equation has a global solution on $[a,b)$. (English) |
| Keyword:
|
generalized Riccati differential equation |
| Keyword:
|
global solutions |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 07396180 |
| idMR:
|
MR4306174 |
| DOI:
|
10.5817/AM2021-3-151 |
| . |
| Date available:
|
2021-07-30T12:27:43Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149018 |
| . |
| Reference:
|
[1] Došlý, O., Řehák, P.: Half-linear differential equations.North-Holland, Elsevier, Amsterdam, 2005. Zbl 1090.34001, MR 2158903 |
| Reference:
|
[2] Erbe, L.: Integral comparison theorems for scalar Riccati equations and applications.Canad. Math. Bull. 25 (1982), 82–97. MR 0657656, 10.4153/CMB-1982-012-8 |
| Reference:
|
[3] Hasil, P.: Conditional oscillation of half-linear differential equations with periodic coefficients.Arch. Math. (Brno) 44 (2008), 119–131. MR 2432849 |
| Reference:
|
[4] Hasil, P., Veselý, M.: Oscillation and non-oscillation of half-linear differential equations with coefficients having mean values.Open Math. 16 (1) (2018), 507–521. MR 3800645, 10.1515/math-2018-0047 |
| Reference:
|
[5] Jaroš, J., Kusano, T., Tanigawa, T.: Nonoscillatory solutions of planar half-linear differential systems: a Riccati equation approach.EJQTDE 92 (2018), 1–28. MR 3884523 |
| Reference:
|
[6] Mirzov, J.D.: Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 14 (2004), 175 pp. Zbl 1154.34300, MR 2144761 |
| Reference:
|
[7] Stafford, R.A., Heidel, J.W.: A new comparison theorem for scalar Riccati equations.Bull. Amer. Math. Soc. 80 (1974), 754–757. MR 0342771, 10.1090/S0002-9904-1974-13588-3 |
| Reference:
|
[8] Travis, C.C.: Remarks on a comparison theorem for scalar Riccati equations.Proc. Amer. Math. Soc. 52 (1975), 311–314. MR 0377188, 10.1090/S0002-9939-1975-0377188-X |
| . |
