Title:
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Comparison results for two-dimensional half-linear cyclic differential systems (English) |
Author:
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Jaroš, Jaroslav |
Author:
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Takaŝi, Kusano |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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53 |
Issue:
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3 |
Year:
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2017 |
Pages:
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131-140 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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half-linear differential systems |
Keyword:
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Picone identity |
Keyword:
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Sturmian comparison |
MSC:
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34C10 |
idZBL:
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Zbl 06819520 |
idMR:
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MR3708767 |
DOI:
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10.5817/AM2017-3-131 |
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Date available:
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2017-09-13T09:30:28Z |
Last updated:
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2020-01-05 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/146878 |
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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:
|
[4] Jaroš, J.: Wirtinger inequality and nonlinear differential systems.Arch. Math. (Brno) 49 (2013), 35–41. Zbl 1299.34124, MR 3073014, 10.5817/AM2013-1-35 |
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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Reference:
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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:
|
[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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[13] Reid, W.T.: Sturmian Theory for Ordinary Differential Equations.Appl. Math. Sci., vol. 31, Springer, New York, 1980. Zbl 0459.34001, MR 0606199 |
Reference:
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[14] Rostás, K.: Comparison theorems for pseudoconjugate points of half-linear ordinary differentialequations of the second order.Acta Math. Univ. Comenian. (N.S.) 72 (2003), 223–228. MR 2040908 |
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