Comparison results for two-dimensional half-linear cyclic differential systems

Jaroslav Jaroš; Kusano Takaŝi

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 3, page 131-140
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Jaroš, Jaroslav, and Takaŝi, Kusano. "Comparison results for two-dimensional half-linear cyclic differential systems." Archivum Mathematicum 053.3 (2017): 131-140. <http://eudml.org/doc/294136>.

@article{Jaroš2017,
abstract = {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.},
author = {Jaroš, Jaroslav, Takaŝi, Kusano},
journal = {Archivum Mathematicum},
keywords = {half-linear differential systems; Picone identity; Sturmian comparison},
language = {eng},
number = {3},
pages = {131-140},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Comparison results for two-dimensional half-linear cyclic differential systems},
url = {http://eudml.org/doc/294136},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Jaroš, Jaroslav
AU - Takaŝi, Kusano
TI - Comparison results for two-dimensional half-linear cyclic differential systems
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 3
SP - 131
EP - 140
AB - 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.
LA - eng
KW - half-linear differential systems; Picone identity; Sturmian comparison
UR - http://eudml.org/doc/294136
ER -

References

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  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. (2015) Zbl1336.34053MR3348046
  3. Elbert, Á., A half-linear second order differential equation, Colloq. Math. Soc. János Bolyai 30 (1979), 153–180. (1979) MR0680591
  4. Jaroš, J., 10.5817/AM2013-1-35, Arch. Math. (Brno) 49 (2013), 35–41. (2013) Zbl1299.34124MR3073014DOI10.5817/AM2013-1-35
  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. (1999) Zbl0926.34023MR1711081
  6. Jaroš, J., Kusano, T., 10.14232/ejqtde.2016.1.100, Electron. J. Qual. Theory Differ. Equ. 100 (2016), 1–10. (2016) MR3568335DOI10.14232/ejqtde.2016.1.100
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  8. Kreith, K., Oscillation theory, Lecture Notes in Math., vol. 324, Springer, 1973. (1973) Zbl0258.35001
  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. (1995) Zbl0873.34020MR1362999
  10. Mirzov, J.D., 10.1016/0022-247X(76)90120-7, J. Math. Anal. Appl. 53 (1976), 418–425. (1976) Zbl0327.34027MR0402184DOI10.1016/0022-247X(76)90120-7
  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. (2004) Zbl1154.34300MR2144761
  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. (1910) MR1556637
  13. Reid, W.T., Sturmian Theory for Ordinary Differential Equations, Appl. Math. Sci., vol. 31, Springer, New York, 1980. (1980) Zbl0459.34001MR0606199
  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. (2003) MR2040908

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