Solutions of Riemann–Weber type half-linear differential equation

Ondřej Došlý

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 1, page 49-61
  • ISSN: 0044-8753

Abstract

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We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case.

How to cite

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Došlý, Ondřej. "Solutions of Riemann–Weber type half-linear differential equation." Archivum Mathematicum 053.1 (2017): 49-61. <http://eudml.org/doc/287960>.

@article{Došlý2017,
abstract = {We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case.},
author = {Došlý, Ondřej},
journal = {Archivum Mathematicum},
keywords = {Riemann–Weber half-linear differential equation; principal solution; modified Riccati equation; asymptotic formula; half-linear second-order difference equations; recessive solution; generalized zero; oscillation; conjugation},
language = {eng},
number = {1},
pages = {49-61},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Solutions of Riemann–Weber type half-linear differential equation},
url = {http://eudml.org/doc/287960},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Došlý, Ondřej
TI - Solutions of Riemann–Weber type half-linear differential equation
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 1
SP - 49
EP - 61
AB - We establish an asymptotic formula for a pair of linearly independent solutions of the subcritical Riemann–Weber type half-linear differential equation. We also complement the results of the author and M. Ünal, Acta Math. Hungar. 120 (2008), 147–163, where the equation was considered in the critical case.
LA - eng
KW - Riemann–Weber half-linear differential equation; principal solution; modified Riccati equation; asymptotic formula; half-linear second-order difference equations; recessive solution; generalized zero; oscillation; conjugation
UR - http://eudml.org/doc/287960
ER -

References

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  1. Agarwal, R.P., Grace, S.R., O’Regan, D., Oscillation Theory of Second Order Linear, Half-Linear, Superlinear and Sublinear Differential Equations, Kluwer Acad. Publ., Dordrecht, Boston, London, 2002. (2002) MR2091751
  2. Došlý, O., Elbert, Á., Integral characterization of principal solution of half-linear differential equations, Studia Sci. Math. Hungar. 36 (2000), 455–469. (2000) MR1798750
  3. Došlý, O., Fišnarová, S., 10.1016/j.na.2010.07.049, Nonlinear Anal. 73 (2010), 3756–3766. (2010) Zbl1207.34041MR2728552DOI10.1016/j.na.2010.07.049
  4. Došlý, O., Řehák, P., Half-Linear Differential Equations, vol. 202, North-Holland Mathematical Studies, Elsevier, Amsterdam, 2005. (2005) Zbl1090.34001MR2158903
  5. Došlý, O., Ünal, M., 10.1007/s10474-007-7120-4, Acta Math. Hungar. 120 (2008), 147–163. (2008) Zbl1199.34169MR2431365DOI10.1007/s10474-007-7120-4
  6. Došlý, O., Yamaoka, N., Oscillation constants for second-order ordinary differential equations related to elliptic equations with p -Laplacian, Nonlinear Anal. 113 (2015), 115–136. (2015) Zbl1375.34051MR3281849
  7. Elbert, Á., A half-linear second order differential equation, Qualitative theory of differential equations, Vol. I, II (Szeged, 1979), Colloq. Math. Soc. János Bolyai, 30, North-Holland, Amsterdam, New York, 1981, pp. 153–180. (1981) Zbl0511.34006MR0680591
  8. Elbert, Á., Schneider, A., 10.1007/BF03322512, Results Math. 37 (2000), 56–83. (2000) Zbl0958.34029MR1742294DOI10.1007/BF03322512
  9. Hartman, P., Ordinary Differential Equations, John Willey and Sons, Inc., New York, London, Sydney, 1974. (1974) MR0171038
  10. 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). (2004) Zbl1154.34300MR2144761

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