| Title:
|
Comparison results for two-dimensional half-linear cyclic differential systems (English) |
| Author:
|
Jaroš, Jaroslav |
| Author:
|
Takaŝi, Kusano |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
131-140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Two identities of the Picone type for a class of half-linear differential systems in the plane are established and the Sturmian comparison theory for such systems is developed with the help of these new formulas. (English) |
| Keyword:
|
half-linear differential systems |
| Keyword:
|
Picone identity |
| Keyword:
|
Sturmian comparison |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 06819520 |
| idMR:
|
MR3708767 |
| DOI:
|
10.5817/AM2017-3-131 |
| . |
| Date available:
|
2017-09-13T09:30:28Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146878 |
| . |
| Reference:
|
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| Reference:
|
[2] Dosoudilová, M., Lomtatidze, A., Šremr, J.: Oscillatory properties of solutions to certain two-dimensional systems of non-linear ordinary differential equations.Nonlinear Anal. 120 (2015), 57–75. Zbl 1336.34053, MR 3348046 |
| Reference:
|
[3] Elbert, Á.: A half-linear second order differential equation.Colloq. Math. Soc. János Bolyai 30 (1979), 153–180. MR 0680591 |
| Reference:
|
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| Reference:
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[5] Jaroš, J., Kusano, T.: A Picone-type identity for second order half-linear differential equations.Acta Math. Univ. Comenian. (N.S.) 68 (1999), 137–151. Zbl 0926.34023, MR 1711081 |
| Reference:
|
[6] Jaroš, J., Kusano, T.: Elbert-type comparison theorems for a class of nonlinear Hamiltonian systems.Electron. J. Qual. Theory Differ. Equ. 100 (2016), 1–10. MR 3568335, 10.14232/ejqtde.2016.1.100 |
| Reference:
|
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| Reference:
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[8] Kreith, K.: Oscillation theory.Lecture Notes in Math., vol. 324, Springer, 1973. Zbl 0258.35001 |
| Reference:
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[9] Li, H.J., Yeh, C.C.: Sturmian comparison theorem for half-linear second order differential equations.Proc. Roy. Soc. Edinburgh Sect. A 125A (1995), 1193–1204. Zbl 0873.34020, MR 1362999 |
| Reference:
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[10] Mirzov, J.D.: On some analogs of Sturm’s and Kneser’s theorems for nonlinear systems.J. Math. Anal. Appl. 53 (1976), 418–425. Zbl 0327.34027, MR 0402184, 10.1016/0022-247X(76)90120-7 |
| Reference:
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[11] Mirzov, J.D.: Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., Mathematica, vol. 14, Masaryk University Brno, 2004. Zbl 1154.34300, MR 2144761 |
| Reference:
|
[12] Picone, M.: Sui valori eccepzionali di un parametro da cui dipende un’ equazione differenziale ordinaria del secondordine.Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) II (1910), 1–141. MR 1556637 |
| Reference:
|
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| Reference:
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| . |
