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Title: Solutions of Riemann–Weber type half-linear differential equation (English)
Author: Došlý, Ondřej
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 53
Issue: 1
Year: 2017
Pages: 49-61
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: Riemann–Weber half-linear differential equation
Keyword: principal solution
Keyword: modified Riccati equation
Keyword: asymptotic formula
MSC: 34C10
idZBL: Zbl 06738498
idMR: MR3636681
DOI: 10.5817/AM2017-1-49
Date available: 2017-03-23T10:06:41Z
Last updated: 2018-01-10
Stable URL:
Reference: [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. MR 2091751
Reference: [2] Došlý, O., Elbert, Á.: Integral characterization of principal solution of half-linear differential equations.Studia Sci. Math. Hungar. 36 (2000), 455–469. MR 1798750
Reference: [3] Došlý, O., Fišnarová, S.: Half-linear oscillation criteria: Perturbation in term involving derivative.Nonlinear Anal. 73 (2010), 3756–3766. Zbl 1207.34041, MR 2728552, 10.1016/
Reference: [4] Došlý, O., Řehák, P.: Half-Linear Differential Equations.vol. 202, North-Holland Mathematical Studies, Elsevier, Amsterdam, 2005. Zbl 1090.34001, MR 2158903
Reference: [5] Došlý, O., Ünal, M.: Conditionally oscillatory half-linear differential equations.Acta Math. Hungar. 120 (2008), 147–163. Zbl 1199.34169, MR 2431365, 10.1007/s10474-007-7120-4
Reference: [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. Zbl 1375.34051, MR 3281849
Reference: [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. Zbl 0511.34006, MR 0680591
Reference: [8] Elbert, Á., Schneider, A.: Perturbations of the half-linear Euler differential equation.Results Math. 37 (2000), 56–83. Zbl 0958.34029, MR 1742294, 10.1007/BF03322512
Reference: [9] Hartman, P.: Ordinary Differential Equations.John Willey and Sons, Inc., New York, London, Sydney, 1974. MR 0171038
Reference: [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). Zbl 1154.34300, MR 2144761


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